Eye_in_the_Sky said:
Each one's outcome is 'nonseparable' from the setting of the other; therefore, the joint-state of their instruments is 'nonseparable'.
Eye,
I've no idea where you're going with all of this and I think you're making things more complicated than they need to be.
Let's backpedal a bit and think about what the Bell analysis is all about. Let's pretend that QM hasn't been invented yet. We know nothing about 'separable' or 'non-separable' or 'wavefunctions'.
Now we have some experiment consisting of 2 pieces of measuring kit and some source. So in the usual fashion we arrange them like so
A <---------- S ----------> B
We can adjust the dial on the kit to measure at settings a,b, or c.
The outcome is just a single binary value 1 or 0 (a ping or a ding)
Everything is at 'black box' level. The only data we can record at each measuring station, for each timeslot, is the setting (a,b, or c) and the binary value obtained.
Our job is to see whether any correlations that might be observed can be explained at this very general level in terms of probability distributions that can actually be measured in this experiment.
So we quite naturally make the assumption that whatever the source is doing or generating (fields, particles, little green tribbles, etc) there are going to be some variables that will explain any correlation. We might not have any control of or access to these variables, but we assume they are underlying things and giving rise to the correlation. Furthermore we quite naturally assume that these variables are such that they have some existence independent of the measurement.
Now, it would be strange if A and B were miles apart and the results (the ping or ding) recorded at A depended in some way on the position of the dial (a,b or c) that had been chosen at B.
Let's call these kinds of variables 'classical-like' - they have properties that are very natural and reasonable. They exist outside of measurement, for one, and they don't bugger up relativity.
Now we write down the various conditional probabilities we have, do some manipulations, and find that there's a constraint on certain functions that can actually be measured in this experiment. So we know that ANY theory that utilises these kinds of variables must give predictions within these constraints.
We do the experiment and find that the results we get don't satisfy this constraint. So whatever is happening (fields, particles or tribbles) it cannot be described by a theory of this kind using these kinds of classical-like variables.
As soon as you want to try to describe things in terms of variables that have some existence independent of measurement (like everyday classical variables such as position or momentum or field strength and so on) then if you want to explain the observed results those variables have to have some non-local connection - crudely put, there must be some mechanism that transfers 'information' about settings at A to the system (kit plus tribble) at B in a way that buggers up relativity. You can't actually communicate FTL, in the sense that A and B can't use this to exchange information, but quite clearly real information about whether A has chosen a,b or c must be, in some sense 'accessible' to the kit plus tribble at B if we want to have our variables have some meaning independent of experiment.
So when you talk of the kit being 'non-separable' are you trying to understand things in terms of variables that have some objective existence outside of measurement and using 'non-separable' to describe this necessary 'information transfer mechanism'? Or do you mean something more akin to the non-separability described by QM?