So I've been thinking about J.S. Bell's
"Introduction to the hidden-variable question" (1971).
See
https://cds.cern.ch/record/400330/files/CM-P00058691.pdfIt's only a few pages long. But in those few pages Bell manages to say quite a lot.
I think this is also the second paper where he suggests doing an experiment that would prove either that there is something wrong with quantum mechanics or that there are no local hidden variables in quantum mechanics.
The paper is divided into four sections.
The first part explains what he's trying to do, ie. why he thinks hidden-variables are so important.
He gives three motivations for being interested in hidden-variable interpretations of quantum mechanics.
(a) He points out the great difficulty we are having defining the boundary between the classical world and the quantum mechanical world. And he guesses that most likely the real world is either all classical or all quantum mechanical. And that would mean that one of the two is an approximation of reality. And he points out, by the way, how much trouble we are in, in terms of understanding the world around us, if the world is all quantum mechanics.
So for instance if there are hidden-variables then that would remove the observer from the central role in physics that the observer plays in the Copenhagen interpretation of quantum mechanics.
(b) He points out that if the hidden-variables exist then we can basically turn quantum mechanics into something like a classical theory.
(c) He points out that there are parts of quantum mechanics, ie. specifically entangled particles, that look they might be, in a sense, hidden-variables.
In the second part of the paper he criticizes J von Neumann's reasoning in one part of von Neumann's paper,
"Mathematische Grundlagen der Quantenmechanik" (1932). Bell starts by objecting to how von Neumann reasoned about some of the math. To oversimplify, Bell thinks that Neumann oversimplified the issue and that von Neumann's logic doesn't prove von Neuman's conclusion that a hidden-variables don't work, or to say it another way that one can't build a consistent interpretation of quantum mechanics from hidden variables.
Bell points out that it's trivially easy to construct an ad hoc hidden-variable scheme for any given experiment. But it's very hard to come up with a comprehensive and consistent interpretation along these lines.
In the third part of his essay, Bell attempts to come up with a comprehensive and consistent local hidden-variable interpretation. Up to a certain point, it goes well, although as usual there's the problematic lack of definition of what a 'measurement' is. Or to quote J.S. Bell:
But it is just at this point that the notoriously vague "reduction of the wave packet" intervenes, at some ill-defined time, and we come up against the ambiguities of the usual theory, which for the moment we aim only to reinterpret rather than to replace. It would be very interesting to go beyond this point. But we will not make the attempt here, for we will find a very striking difficulty at the level to which the scheme has been developed already.
And so we arrive at part four of Bell's essay where he explains the difficulty with a consistent and comprehensive local hidden-variable interpretation for quantum mechanics.
Skipping the math, if you assume the existence of local hidden-variables and also that the math of quantum mechanics is correct, then you get a contradiction.
And it should be possible to actually see this contradiction or not, in a sense, by experiment.
The problem with actually conducting the experiment at that time was that it required a very low error rate. Or to put it another way, there seems to be a lot of noise in these actual experiments.
In any case there is a certain parallel between the experiment that J.S. Bell suggested in 1966 and the experiment that Jonathan Oppenheim suggested more recently. It's not the same experiment, but both are kind of about the boundaries between the classical and quantum. And note it's an unusual situation to have, in this context, where the theorists are able to suggest an actual experiment.