Beable-guided measurement theory

TL;DR

This paper explores the origin of quantum randomness within de Broglie-Bohm theory, proposing a thought experiment involving beable-parameters that may violate uncertainty relations, and identifies models where fluctuations can be neglected.

Contribution

It introduces a detailed analysis of quantum randomness emergence in de Broglie-Bohm theory and proposes a novel thought experiment testing beable-parameters and their fluctuations.

Findings

Quantum randomness arises from stochastic fluctuations of beable parameters.

Certain models show fluctuations can be neglected, challenging standard assumptions.

The proposed thought experiment tests the possibility of information transition violating uncertainty.

Abstract

In quantum mechanics, randomness is postulated as a separate axiom. De Broglie's theory allows one to reproduce quantum phenomena from completely deterministic formalism. But the question of the quantum randomness emergency in the de Broglie-Bohm theory needs special attention. In the work [G. Tastevin, F. Lalo\"e, Comptes Rendus. Physique, 2021, 22, 1, pp. 99-116], it was shown that it arises as a result of the device microscopic state influence on the measurement result. In our work, we investigate the genesis of the quantum randomness in the de Broglie's theory in more details. Namely, we investigate the target system and the device behaviour in the decoherence process and model the measurement of canonical-conjugate observables. We propose a thought experiment which tests the opportunity of the information transition using beable-parameters violating the uncertainty relation. We show that in the measurement process, the strong stochastic fluctuations of beable parameters arise randomising the system in accordance with the uncertainty relation. Nevertheless, we find anomalous models of measurement in which these fluctuations can be neglected. These special models require further investigation.