EPRB and independent vs dependent variables

[Xray]

… a variable cannot be both dependent and independent at the same time.

Tom, not wanting to sidetrack other threads:

Let Xi + Yi = 0, (1)

where Xi and Yi (hidden random-variables in EPRB; i = 1, 2, …, N) are pairwise correlated by the conservation of angular momentum.

Alice can choose Xi as the independent variable, so Yi is her dependent variable.

Bob can choose Yi as the independent variable, so Xi is his dependent variable.

So: Do we need to qualify your --- "a variable cannot be both dependent and independent at the same time" --- by saying: the notion of dependence or independence is reference-frame dependent?

Tks, Xray

[thray]

Xray wrote: "Do we need to qualify your --- 'a variable cannot be both dependent and independent at the same time' --- by saying: the notion of dependence or independence is reference-frame dependent?"

I would rather say it's event dependent, i.e., time-indexed by the initial condition.

As Karl Hess (Einstein was Right!) explained:

The requirement of equal outcomes for equal setting and random outcomes for a given measurement station is also the Achilles' heel of Bell's work, because equal settings do not appear in his inequality and require different measurements with different space-time coordinates compared to the measurements for non-equal setting pairs." (p. 172)

This is a necessary consequence of continuous spacetime defining boundary conditions for a continuous function. The "equally likely" hypothesis that attends all probabilistic theories does not apply.

Best,

Your cousin Tom

[thray]

Here's another, probably more complete, description from the recent paper by Hess, de Raedt and Michielson:

" ... counterfactual definiteness restricts the use of variables to those that can be independently picked from their respective domains. However, a magnet- or polarizer- orientation, mathematically represented by the variable j, cannot be picked independently of the measurement times, which are mathematically represented by t_n and registered by the clocks of the measurement stations. Once a setting is picked at a certain space-time coordinate, no other setting can be linked to that coordinate, because of the relativistic limitations for the movement of massive bodies and the fact that Bell’s theory is confined to the realm of Einsteinian physics and, therefore, excludes quantum superpositions. Thus any measurement is related to spatio-temporal equipment changes and the mathematical variables that describe the measurement need to represent the possible physical situations."

That won't work with Bell-Aspect.