In our discussion of the Bell inequality, we saw that an ideal test of locality would require that we study a two-body decay of some composite system like, for example, a diatomic molecule. The experiments most widely claimed as evidence for Bell-inequality violation use, instead of a diatomic molecule, an atom which has been excited in such a way that it emits two simultaneous light signals of different colours. This overall process is known as an atomic cascade. It is not a two-body decay. At best it can be considered a three-body decay - that is the excited atom decays into a less excited atom plus two "photons" - but this is not at all convincing, since, as I have indicated elsewhere, photons are not proper bodies!
The following two references cover all experiments of this type up to 1985. There have been none since.
There are many well known "loopholes" in all of these experiments. The most important one was identified as long ago as 1970, and is called the Enhancement Loophole. It arises because less than one per cent of the atomic-cascade or PDC pairs emitted are actually detected, so certain highly model-dependent assumptions have to be made about the statistical sampling. All the QM experts know about this loophole, but they are remarkably coy about informing the general public. Two key references are
My collaborators and I have shown that the enhancement loophole is really much more than a loophole! The zeropoint electromagnetic field can systematically enhance a weak atomic light signal to give, in a natural and entirely local manner, the observed violation of a homogeneous Bell inequality. Only inhomogeneous Bell inequalities may be used as a test of local realism, and nobody has ever reported a violation of these. Here are some references to our work
The latter article is suitable for the nontechnical reader and is available by email.