Clauser-Horne-Shimony response to Bell's theorem

[bascule]

I've recently found an extremely interesting bit of writing by John Bell (of Bell's Inequality) that I'd like to share:

 

http://books.google.com/books?id=FGnnHxh2YtQC&pg=PA100&lpg=PA100&ots=3qT9MVkq-6&sig=1HGVjQN12sbTUoJ-qK_pz3g4qGU#PPA103,M1

 

Consider the extreme case of a 'random' number generator which is in fact perfectly deterministic in nature - and, for simplicity, perfectly isolated. In such a device the complete final state perfectly determines the complete initial state - nothing is forgotten. And yet for many purposes, such a device is precisely a 'forgetting machine'. A particular output is the result of combining so many factors, of such a lengthy and complicated dynamical chain, that it is quite extraordinarily sensitive to minute variations of any one of many initial conditions. It is the familiar paradox of classical statistical mechanics that such exquisite sensitivity to initial conditions is practically equivalent to complete forgetfulness of them. To illustrate the point, suppose that the choice between two possible outputs, corresponding to a and a', depended on the oddness or evenness of the digit in the millionth decimal place of some input variable. Then fixing a or a' indeed fixes something about the input - i.e., whether the millionth digit is odd or even. But this peculiar piece of information is unlikely to be the vital piece for any distinctively different purpose, i.e., it is otherwise rather useless. With a physical shuffling machine, we are unable to perform the analysis to the point of saying just what peculiar feature of the input is remembered in the output. But we can quite reasonably assume that it is not relevant for other purposes. In this sense the output of such a device is indeed a sufficiently free variable for the purpose at hand. For this purpose the assumption is then true enough, and the theorem follows.

 

Arguments of this kind are advanced by CHS in defending the corresponding assumption in the Clauser-Horne analysis. I do not know why they should be considered less relevant here.

 

Of course it might be that these reasonable ideas about physical randomizers are just wrong - for the purpose at hand. A theory may appear in which such conspiracies inevitably occur, and these conspiracies may then seem more digestible than the non-localities of other theories. When that theory is announced I will not refuse to listen, either on methodological or other grounds. But I will not myself try to make such a theory.

 

It's interesting to see Bell talking about these kinds of ideas. Can anyone provide me with further background on Clauser-Horne-Shimony or your interpretation thereof?