The paradoxical nature of reality (and Mermin's simplified one) that we have seen in part 1, part 2, part 3, part 4 and part 5 of this series seems so only because of an assumption called contra-factual definiteness or CFD. What nature and the function of Mermin's machines shows us is that every quantum theory must either violate locality or CFD.
But if nature is allowed to be non-local that would be magic, i.e. faster than light information-sending magic (just like the universe reading the experimenters' minds is magic or runs of endless perfect luck is magic).
To resolve things we must turn to the "many worlds"-interpretation of quantum mechanics. Many-worlds with its multiplicity of results in different worlds violates CFD, of course, and thus can be local. Thus many-worlds is the only local quantum theory in accord with the standard predictions of QM and, so far, with experiment.
THE VIOLATION OF CONTRA-FACTUAL DEFINITENESS
Bill Taylor: "It is, of course, to MWI that we must turn. Or, as I insist, better-called MOI - the many objects theory. Talk of worlds is confusing at best and mystical at worst. All that happens is that whenever a Particle has an option of different possible things to do, it does them ALL, so that there are many particles following on from the one Particle there was, that made the choice. These two or more (usually gazillions) of subsequent alternative particles are far apart, not in the 3 spatial dimensions, but in invisible dimensions (modelled as the Hilbert space of operator outcomes), so they do not interact. i.e. if we SEE one of them, we won't see any others. The others are still there, buzzing along right alongside (usually) the one we do see, but quite indetectable by any means. For the brief start of their journeys they all (appear to) affect one another - that usually being called interference, but usually they quickly move far apart (Hilbertly) unless huge efforts are made in labs to bring them back close again.
And, crucially, the different particles produce gazillions of
other particles of any type they hit. So if there were two
particles coming out of some bipartite experiment, when they
are absorbed and detected by a photomultiplier (or eye), that
multiplier is split into two, perhaps recording different
properties, and that in turn will split any watching experimenters
into two, and so on "by contagion" throughout the universe;
(all this is what is called the "relative state" part of
the explanation). So, no new worlds, but an irregularly
expanding globe of differently H-spaced objects, which almost
never again can meet. As I like to call it, MWI is the logical
and scientific theory of ghosts!
OC all this is a little(!) hard to swallow, until you get used
to seeing things in the proper light, (whereupon it becomes
amazingly simple and clear-cut!); and so probably even now most
of the science world refuses to take it on board. The general
public has probably barely heard of it, and you can be sure that
popularizers and sci-fi authors have all got it badly wrong."
Next time we will see how this solves the problem with Mermin´s faux-EPR machines and just about everything else as well.