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A Prediction Loophole in Bell's Theorem

John R. Dixon

Published Mar 1, 2011• 1 citation
OpenAlex

Abstract

We consider the Bell’s Theorem setup of Gill et. al. (2002). We present a “proof of concept” that if the source emitting the particles can predict the settings of the detectors with sufficiently large probability, then there is a scenario consistent with local realism that violates the Bell inequality for the setup.

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Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.
Bell's theorem is an important milestone in the development of quantum mechanics. It draws a line between concepts such as realism and locality on the one hand and quantum mechanics on the other. Experimentally veried violations of Bell inequalities can yield important information about what assumptions can be made about physical reality. Experiments have been conducted for over 40 years, but have left loopholes open in their executions. It is of great interest to close these loopholes, and in order to do so, further experiments are needed. The objective of this project is to investigate the underlying, previous work in the eld and to formulate a proposal for a new experiment. To do this, the derivations of the original Bell inequality and the CHSH inequality are presented along with previously conducted experiments. Also presented is the EPR paradox from which sprung the original Bell inequality.
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of entangled pairs of spin-1/2 particles we propose an alternative measurement setup which is consistent to the necessary assumptions corresponding to the derivation of the Bell inequalities. We find that the Bell inequalities are never violated with respect to our suggested measurement process.