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

Abstract

In the derivation of Bell's inequalities, Bell supposed that joint probability distribution is only a function of hidden variable. It has been shown that Bell's inequalities fail if this assumption does not hold. Other researches show that Bell's locality implies independence of two measurement events. We point out that the measurements of EPR pairs may be 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 is the combination of circularly or linearly polarized photon pair under appropriate conditions, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of 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 pairs. The last one uses successive measurement 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.