Zafa Pi said:
I was searching on line for a couple hours and I find a quagmire of definitions of local and non-local whether physics is one or the other, which interpretations are one or the other, if realism or CFD is given up only then do we have non-locality, or maybe non-locality is always there. So many disagree with one another and everybody is sure.
Yes indeed, and it's rather easy to tie one's philosophical knickers in all sorts of knots worrying about the nuances of all the terms that get bandied about; locality, Einstein locality, Bell locality, causality, Einstein locality, signal locality, CFD, non-contextuality, realism and so on ad nauseam. I suppose it gives the philosophically minded something to do on a long winter's evening and keeps them off the streets.
I am, of course, being overly unkind here in order to make a point. The words, divorced from the analyses that spawned them, can so easily lead one astray. That's why I personally feel it's so important to ground oneself in the actual specific analysis and see what the terms actually mean - instead of trying to wade through pages of overblown rhetoric that obfuscate rather than elucidate.
So my advice is to take a derivation of a BI that you like and pick it apart. My own favourite is Bell's wonderful analysis of the CHSH inequality that is contained in his Bertlmann's socks paper. Bell's original inequality is in fact a special case of the more general CHSH version. It's the ideas and the physics in the analysis, rather than what we call these things, that is important I feel. So, sure, one author might use the term 'locality' whereas another might call the same thing 'Bell locality', or even 'Einstein causality', but underlying it all are the same ideas that are more clearly expressed in symbols. In an ideal world it would be nice if we could all agree on the same nomenclature, or even use nomenclature consistently - but we're all human and often try to cut corners and use shorthand.
So let's take the CHSH version and see what is involved.
(1) we have an experiment that allows us, after sufficiently many runs, to measure to a good approximation the joint conditional distributions ##P(A,B | a,b)##
(2) we wish to attempt to explain the correlations and so we
assume that there are some extra variables or quantities, all lumped into the symbol ##\lambda## for convenience, that explain the correlations in the following sense ##P(A,B | a,b, \lambda) = P(A | a,b, \lambda)P(B | a,b, \lambda)##. The physical meaning here is that these extra variables, ##\lambda##, account for the observed correlation so that any
residual fluctuation in the measured quantities must be independent
But look at ##P(A | a,b, \lambda)## here, for example. It's telling us that the distribution of results obtained by Alice is dependent on the setting chosen by Bob at some remote location. How can that be? It would seem to run counter to our intuition and, if it were true, if we could also control the variables ##\lambda## it would certainly allow us to construct a FTL signalling scheme where we could transmit real information faster than we could send the information using light.
In order to avoid this unwelcome possibility (at least) the further assumption is made that :
(3) ##P(A,B | a,b, \lambda) = P(A | a,b, \lambda)P(B | a,b, \lambda) = P(A | a, \lambda)P(B | b, \lambda)##.
The last step on the RHS is where the 'locality' considerations get imposed. Physically we're saying that the distribution of results at Alice depends only on Alice's setting, and the hidden variables - and do not depend on the choice of device setting at some remote place. Physics would be very strange indeed if we allowed this to be so - if the experiments we do here depend on whether someone a million miles away has twiddled with his knob or not we'd never be able to trust the results we obtained in our laboratory. Intuitively we can see that the only way for this to happen is if information about a device setting at some remote location was communicated (in some fashion) to our lab. Somehow our own system (device + measured object) must 'know' about some remote knob twiddling. That definitely doesn't seem right does it?
Apart from the purposes of communication and using consistent terminology does it really matter whether we term condition (3) 'locality', or 'Bell locality', or 'the anti knob-twiddling postulate'? The meaning and intent is crystal clear in the analysis - it can become less clear when we abstract this idea out of the analytical context and try to reason about it. But as long as we continually reference back to our grounded experiment (hypothetical or otherwise) and the assumptions we use in order to construct a plausible model, then everything should be clear enough - even if different people use the same words in subtly different ways.