Exploring the foundations of quantum mechanics using Monte Carlo simulations of the Freedman-Clauser experimental test of Bell's Inequality

TL;DR

This study uses Monte Carlo simulations to compare different models of wave function collapse against experimental results from Bell's Inequality tests, highlighting the accuracy of quantum and dynamical collapse models.

Contribution

It introduces detailed Monte Carlo simulations of the Freedman-Clauser experiment to evaluate wave function collapse models and estimate the correlation length in dynamical models.

Findings

Quantum mechanical calculations closely match experimental data for certain angles.

Local realistic models do not replicate experimental results accurately.

Dynamical state reduction models approximate quantum results within 1% and estimate correlation length.

Abstract

Monte Carlo simulations of the Freedman-Clauser experiment are used to test the generic wave function collapse model of Quantum Mechanics, a local realistic model, and a dynamical state reduction model of wave function collapse. The simulated results are compared to the actual results of the experiment which confirmed the quantum mechanical calculation for nine different relative angles between the two polarization analyzers. For each simulation $5\times10^7$ total simulated photon pairs were generated at each relative angle. The generic wave function collapse model closely followed the general shape of the theoretical calculation but differed from the calculated values by 2.5% to 3.3% for angles less than or equal to $\pi/8$ and differed by 15.0% to 52.5% for angles greater than or equal to $3\pi/8$. The local realistic model did not replicate the experimental results but was generally within 1% of a classical calculation for all analyzer angles. A dynamical state reduction/collapse model, approximated by using a "smeared" polarization, yielded values within 1% of the quantum mechanical calculation and provides an independent estimate of the correlation length used in these models of $r_c = (1.04 \pm 0.14)\times 10^{-5}$ cm.