Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment

TL;DR

This paper introduces a non-Boolean hidden variables model that successfully reproduces quantum mechanics' predictions for Bell's experiment, challenging traditional views on local realism and Bell's inequalities.

Contribution

The paper proposes a novel non-Boolean hidden variables model using vectors and projection operations to reconcile Bell's inequalities violation with local realism.

Findings

Model reproduces Bell test predictions

Reconciles Bell violation with local realism

Highlights need for non-Boolean logic in quantum models

Abstract

The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. Many theories have been proposed to reconcile the violation of Bell's inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that any theory aimed to violate Bell's inequalities must start by giving up Boolean logic. The problem is split in two: the "soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism. The "hard" problem is to predict the time values when single particles are detected. A simple hidden variables model is introduced, which solves the soft problem. This is possible thanks to the use of vectors as the hidden variables and the operation projection, which do not hold to Boolean logic. This model reconciles the violation of Bell's inequalities with Local Realism and should end decades of controversy. Regarding the hard problem, the introduced model is as incomplete as Quantum Mechanics is. It is argued that solving the hard problem involves devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variables as input data and replace the statistical Born's rule with a deterministic threshold condition.