# Are Quantum Models for Order Effects Quantum?

## TL;DR

This paper compares quantum and classical projection models in quantum cognition, finding no advantage of quantum models over classical ones for order effects, and proposes a new interpretation of rotation parameters based on uncertainty.

## Contribution

It demonstrates that quantum projection models do not outperform classical models in order effects and introduces a relativistic interpretation of rotation parameters based on knowledge uncertainty.

## Key findings

- Quantum and classical projection models yield similar results.
- Quantum interference effects are not essential in these models.
- A new interpretation of rotation parameters as uncertainty factors.

## Abstract

The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a $N$-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of the world and towards the context of the questions.