Dynamics and Hidden Variables

TL;DR

This paper investigates how spin 1/2 particles' unitary evolution can be modeled with hidden variables in a counterfactual definiteness framework, revealing limitations in aligning such models with quantum mechanics predictions.

Contribution

It introduces a triplet-based hidden variable model for spin 1/2 evolution and demonstrates its incompatibility with quantum mechanics unless certain assumptions are relaxed.

Findings

The triplet representation can model some unitary evolutions.

The model cannot fully reproduce quantum predictions for entangled states.

Compatibility with quantum mechanics requires dropping some assumptions.

Abstract

We study the way the unitary evolution of spin 1/2 particules can be represented in a counterfactual definiteness setting. More precisely, by representing the state of such a particule by a triplet of values corresponding to the supposedly pre-existing outcomes of some measurements (those corresponding to the three Pauli matrices), we analyse the evolution of our representation when some unitary gates (namely, the Hadamard gate, the \pi/2 phase shifter and the controlled-not) are applied. Then, we describe in terms of triplets the creation of an EPR pair and discuss the possibility of having this representation comply with the predictions of quantum mechanics. Finally, we show that this is not possible unless one of the assumptions used to build our model is dropped.