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.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.

arXiv:1002.4225Journal of Physics A Mathematical and TheoreticalNov 11, 20103 citations

Perspectives on Quantum Reality

Rob Clifton

Springer eBooksJan 1, 1996225 citations

Quantum theory and reality

Robert B. Griffiths

Cambridge University Press eBooksNov 29, 20011 citation

Quantum objective realism

Adam Bednorz

The question of whether quantum measurements reflect some underlying objective reality has no generally accepted answer.We show that a description of such reality is possible under natural conditions such as linearity and causality, although in terms of moments and cumulants of finite order and without relativistic invariance.The proposed construction of observations' probability distribution originates from weak, noninvasive measurements, with detection error replaced by some external finite noise.The noise allows us to construct microscopic objective reality, but remains dynamically decoupled and hence unobservable at the macroscopic level.The question of whether quantum measurements reflect some underlying objective reality has no generally accepted answer.We show that a description of such reality is possible under natural conditions such as linearity and causality, although in terms of moments and cumulants of finite order and without relativistic invariance.The proposed construction of observations' probability distribution originates from weak, noninvasive measurements, with detection error replaced by some external finite noise.The noise allows us to construct microscopic objective reality, but remains dynamically decoupled and hence unobservable at the macroscopic level.

arXiv:1411.0337New Journal of PhysicsSep 10, 20154 citations

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.