On the Implication of Bell's Probability Distribution and Proposed Experiments of Quantum Measurement

TL;DR

This paper challenges the traditional interpretation of Bell's inequalities by emphasizing the role of measurement settings in probability distributions, proposing experiments to explore local hidden variables and the nature of entangled photons.

Contribution

It reinterprets Bell's probability distribution as dependent on measurement settings, argues that Bell's inequalities do not necessarily imply non-locality, and proposes experiments to test local hidden variable theories.

Findings

Bell's inequalities fail when measurement settings are considered in probability distributions.

Local hidden variables could explain EPR experiment results without non-locality.

Proposed experiments aim to test the nature of entangled photon pairs and measurement influences.

Abstract

In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the distribution of the joint measurement outcomes on the two sides. So it is a function of both hidden variable and settings. In this case, Bell's inequalities fail. Our further analysis shows that Bell's locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, thus violation of Bell's inequalities cannot rule out the existence of local hidden variable. In order to explain the results of EPR-type experiments, we suppose that polarization entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any non-local influence on it. Then several experiments are suggested to reveal the components of polarization entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with a same quantum state will behave in the same way under the same measuring condition.