Do Bell and PBR together point toward nonlocal reality?

[bohm2]

This is the part that is still confusing me and relates to one the major assumptions of the PBR theorem and the issue of non-separability brought up by a few papers/authors. This summary contrasting the implications of PBR theorem versus Bell's theorem is taken from one of the author's slide presentations:

Bell’s theorem: Systems have an objective physical state + Experimenter free will + QM → Non-locality

PBR theorem: Systems have an objective physical state + Preparation independence + QM → ψ-ontic

What is the quantum state?
http://www.cs.ox.ac.uk/qisw2012/slides/barrett.pdf

From that slide presentation, it seems that there is a difference between the 2 theorems with respect to the assumptions made (hi-lited in red above) and yet one of the authors in a blog suggests that both Bell's and PBR make the same and seemingly reasonable assumption:

Preparation independence is simply the assumption that we have the ability to build independent, uncorrelated experimental apparatuses to act as preparation devices of microscopic systems, and that any deeper theory of nature than quantum theory will not overthrow this principle by virtue of “hidden super-correlations” where to date scientists have always successfully assumed there are none...We are in a similar position with Bell’s theorem...that theorem relies on a presumed ability to make independent choices of measurements at separated locations. Denial of such is the “super-determinism” loophole, and while intelligent people can and do consider its plausibility, and while it is an important insight into Bell’s theorem that this assumption is necessary, the jury is still out (‘t Hoofts efforts notwithstanding) as to whether a super-deterministic theory agreeing with all experiments to date can even be constructed, never mind be a plausible theory of nature.

Guest Post: Terry Rudolph on Nature versus Nurture
http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/

It seems to me that there is a difference between Experimenter free will vs. Preparation independence or am I mistaken?

 

[Demystifier]

It seems to me that there is a difference between Experimenter free will vs. Preparation independence or am I mistaken?

That's a very good and very subtle question!

It seems to me that the relevant aspects of those two assumptions are essentially the same. Namely, when in the Bell theorem we require that "experimenters have free will", all what we really need is that the choice made by one experimenter is INDEPENDENT on the choice made by another experimenter. These two experimenters choose the directions in which the spins will be measured, so we can say that they PREPARE the measuring devices.

From this point of view, the difference between PBR and Bell lies in the fact that the former requires preparation independence of the two PARTICLES which will be measured, while the latter requires preparation independence of the MEASURING DEVICES for the two particles. Both require preparation independence, but for different objects - the measured system for PBR, or the measuring device for Bell.

Now, if we assume that there is no fundamental difference between measured systems and measuring devices (e.g., that both are ultimately described by quantum mechanics), then these two kinds of preparation independence are actually the same.

 

[Jolb]

These last two posts are very interesting. The superdeterminism loophole is a deep one and often gets overlooked (to the point that most objections to Bell's theorem actually rely on sneakily incorporating superdeterminism), and what Bartlett says in his slides demonstrates a very interesting parallel between PBR and Bell with regards to superdeterminism.