Towards violation of Born's rule: description of a simple experiment

TL;DR

This paper proposes a simple experiment to test potential violations of Born's rule, based on a new classical model of quantum phenomena called PCSFT, which suggests quantum probabilities are only approximate.

Contribution

It introduces an experimental setup to detect deviations from Born's rule predicted by the PCSFT model, challenging the standard quantum mechanical framework.

Findings

Deviations from Born's rule are predicted to be small but detectable.

An experimental amplification method for deviations is proposed.

PCSFT reproduces quantum correlations while allowing for Born's rule violations.

Abstract

Recently a new model with hidden variables of the wave type was elaborated, so called prequantum classical statistical field theory (PCSFT). Roughly speaking PCSFT is a classical signal theory applied to a special class of signals -- "quantum systems". PCSFT reproduces successfully all probabilistic predictions of QM, including correlations for entangled systems. This model peacefully coexists with all known no-go theorems, including Bell's theorem. In our approach QM is an approximate model. All probabilistic predictions of QM are only (quite good) approximations of "real physical averages". The latter are averages with respect to fluctuations of prequantum fields. In particular, Born's rule is only an approximate rule. More precise experiments should demonstrate its violation. We present a simple experiment which has to produce statistical data violating Born's rule. Since the PCSFT-presentation of this experiment may be difficult for experimenters, we reformulate consequences of PCSFT in terms of the conventional wave function. In general, deviation from Born's rule is rather small. We found an experiment amplifying this deviation. We start with a toy example in section 2. Then we present a more realistic example based on Gaussian states with very small dispersion, see section 3.