On fuzzy hidden variables

M. Zisis

Arnold Neumaier

A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries no connotations of unlimited repeatability; hence it can be applied to unique systems such as the universe. Precise concepts and traditional results about complementarity, uncertainty and nonlocality follow with a minimum of technicalities. Probabilities are introduced in a generality supporting so-called effects (i.e., fuzzy events). States are defined as partial mappings that provide reference values for certain quantities. An analysis of sharpness properties yields well-known no-go theorems for hidden variables. By dropping the sharpness requirement, hidden variable theories such as Bohmian mechanics can be accommodated, but so-called ensemble states turn out to be a more natural realization of a realistic state concept. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

Arthur I. Fine, Paul Teller

Jesús Fernández Sánchez

In this paper, it will be explained the quantum entanglement using hidden variables. This means, with no need of immediate or infinity range interactions. For this, the solution would be to take into account also the measurement device hidden variables. These hidden variables of the measurement device will cause that the detection of the particles to be measured, can only be made at certain moments, places and orientations that correspond when the particle states have specific values. This means, the particle state can be changing over time, but the measurement equipment can only detect it when it has certain values (because the hidden values of the measurement equipment are also participating in the process). So, the measurement device is participating indirectly in the entanglement of the particles. The problem until now with hidden variables interpretation was that only the hidden variables of the particles were taken into account. But, once the measurement device hidden variables status is considered also, the issue can be solved.

F.J. Duarte

Koji Nagata, Tadao Nakamura

We study the relation between hidden variables theories and quantum computation.We discuss an inconsistency between a hidden variables theory and controllability of quantum computation.To derive the inconsistency, we use the maximum value of the square of an expected value.We propose a solution of the problem by using new hidden variables theory.Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics.This experiment can be an easy detector to Pauli observable.We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case.Hidden variables theories may not depicture quantum detector.This is a quantum measurement theoretical profound problem.