Let us return to the main topic.
Concerning Stage 2 (post #49), we now have one qualifying degree of
weirdness (post #112, fully justified in post #115) and an expression
of dissatisfaction about trying to quantify weirdness at all (post #98).
Leaving Stage 2 still open for a while, I'll begin with the next stage,
where I promised to state my own interpretation of the experiment,
and why I think the results are not weirder than what one finds
classically in other situations. My interpretation will extend over
two stages: Stage 3, where I make some general remarks that are
independent of what is discussed in Stage 2, and (when Stage 2
is completed) Stage 4, where I use the results of Stages 2 and 3 to
complete my view on the matter.
(Note: Stages 2 and 3 are now also closed for discussion.
Stage 4 begins in
post #187.)
Stage 3 is opened with the following observations, whose discussion
is invited. My observations at this stage are completed in
post #174,
with a discussion of how weirdness and knowledge are related.
In our setting, assume for the moment that the nature of Norbert's
signals are known to everyone, and are of the kind consistent with
quantum mechanics but inconsistent with Bell-type assumptions.
Assume also that there is a human Alice behind the dumb machine Alice.
Under these conditions I want to discuss what the human Alice
knows about Bob's results after she has completed her experiments.
My claim is that she knows nothing definite at all.
For the results Bob gets depend on what he is doing, and she is not
informed about the latter. At best she can draw conditional inferences
''If Bob's pointer position was set to ... then his results were ...''.
This is closer to guesswork of the form we use in medical diagnostics
when decisive facts are absent than to scientific knowledge of the kind
we can find in standard textbooks, and to engineering knowledge encoded
in properly working machines.
The knowledge that Alice has feels more like what we know about an
(ideal) pendulum when its initial conditions are unknown - we know the
general structure of the possible configurations, but we don't know
anything about the configuation itself. If we take the analogy seriously
we conclude that [given Norbert's fixed signalling strategy]
Nature solves an initial-value problem with two inputs
(pointer settings) and two outputs (color of response) - that on Alice's
side and that on Bob's side. The joint output depends on both inputs.
This dependence is Bell's form of nonlocality - demonstrated by this
kind of experiments and quite obvious from this way of thinking about
it, even without an experimental proof by the violation of corresponding
Bell inequalities.
Remarkably, Bell's findings wouldn't have seemed weird at the end of the
19th century - classical field equations such as the heat equation also show
this kind of nonlocality!
Nonlocality is classically intrinsic even to Newtonian mechanics in its
original form where celestial bodies act instantaneously over
arbitraily large distances. It is a standard part of nonrelativistic
classical mechanics. So why should nonlocality count as weird?
Being already manifestly present in nonrelativistic multiparticle
classical mechanics, it is no surprise at all that it is also present in
nonrelativistic multiparticle quantum mechanics such as Bell-type
experiments! Note that essentially all analysis of Bell nonlocality is
done in a nonrelativistic framework! Plus lip service paid to relativity,
in a form that doesn't enter at all into the formulas...
To impose weirdness by invoking arguments involving the speed of light
in an otherwise nonrelativistic framework also makes the heat equation
seem weird since a change in temperature at one place immediately
affects the temperature everywhere else.
... and Newton's celestial mechanics since the change in position of one
celestial body immediately affect the positions everywhere else.
The quibbles with this form of nonlocality are caused by a superficial
understanding of relativity theory and the use of superficial relativity
arguments in an explictly nonrelativistic classical or quantum setting.
What seems to be unnatural or weird is solely due to mixing two
incompatible settings.
If one attempts to disentangle the two settings interesting things happen:
On the purely nonrelativistic level, all weirdness has disappeared;
things are no worse in quantum mechanics than in classical celestial
mechanics or fluid mechanics.
On the other hand, one can try to see what happens when one looks
at classical relativistic multiparticle theories. Once one starts looking for
these (I challenge you to do such a search yourself) one finds that from
the outset, they are plagued with tremendous weirdness!
Clearly, it is the particle picture that - classically! - introduces this
weirdness into relativity theory since classical relativistic field theories
have no problem at all as long as one doesn't introduce point particles
into them. It thus appears that in quantum mechanics of point particles
the classical weirdness is even softened since it appears only in situations
that take a lot of effort to prepare, and disappears completely once one
consistently stays in the realm of quantum field theory.