# Spin and Wind Directions II: A Bell State Quantum Model

## TL;DR

This paper extends a quantum cognitive model of wind direction choices, demonstrating Bell inequality violations while satisfying the marginal law, and addresses criticisms about entanglement in such experiments.

## Contribution

It provides a symmetrized quantum model that explains Bell violations in cognitive data and clarifies misconceptions about entanglement in these contexts.

## Key findings

- Violates CHSH inequality with symmetrized data
- Obeys the marginal law in the quantum model
- Addresses criticisms regarding entanglement in cognitive experiments

## Abstract

In the first half of this two-part article, we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of 'Two Different Wind Directions', and showed that the data violate the CHSH version of Bell's inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.