Dear Wilhelmus de Wilde,
Great comments and great questions! And thanks for the link to "Ghost in the atom". I'll start with that. The animation is actually wrong in my view. They say that if the wave function is 'real' then you get a 'taco-dog-burger' in the box until you look at it. That is the 'collapse of the wave function' interpretation that I explain to be incorrect. It surprises me that physicists can insist that the wave function is real and still believe it is a mathematical superposition.
But I do agree with you (and them) that "the wave function cannot be a mere abstract mathematical device, IT MUST BE REAL" and that "Quantum Theory makes no sense if the wave function is a mere probability distribution, instead, the wave function HAS TO BE A REAL THING."
Recent measurements of the wave function (discussed in my essay) agree with a recent proof by Pusey, Barrett, and Rudolph ('PBR') than an "information only" wave function cannot predict quantum results. This is consistent with the work you mention and with my essay.
I also agree with you that the system has true ('real') properties before it is measured [that is, it is a dog or a taco or a burger before you open the box, not a mysterious 'superposition' taco-dog-burger]. To not believe this leads to the situation I described in "down the rabbit hole" above where the first measurement shows what values the experimenter will choose **in the future**, before they have even made their choice. In other words, acting as if Bell's theorem [or the Copenhagen interpretation] is true leads to nonsense.
You describe the wave as "informing it how to behave". I would not interpret this literally. The particle and physical wave function form one inseparable system. The motion of the particle induces the field that constitutes the wave and changes in the wave feed back to the particle. Neither is "boss".
You propose a universal web of interactions in which every system influences every other system. We know that we have something like this (in the gravitational field, for instance) but the real question is how fast the influences travel. If they travel at the spead of light, then one side of the 'web' may not influence the other side for 14 billion years or so. But what if the changes are instantaneous (as you seem to imply with the word 'simultaneity')? Then every change propagates instantly to every other system, the reaction propagates back immediately, and the reaction-to-the-reaction propagates to all other systems immediately and all possible future changes and all reactions to these changes all happen at once, resulting, I believe, in nothing happening. So there must be a finite speed, but then one is back to such long delays that only local interactions seem to make much sense.
You note that two particles are represented in an abstract 6-dimensional space, three particles in a 9-dimensional space and N particle in a 3N or abstract 'configuration' space. I also treat this is my essay (page 7). Einstein and others, believing that wave could exist *without particles*, concluded that momentum and energy were conserved *only statistically* in 3-space. Schrodinger then FORCED the 3N-dimensional solution to conserve energy (after all, Schrodinger's equation is just the conservation of energy relation, written using operators!) As explained in the essay, this seems to imply (in view of Einstein's confused 'statistical conservation' idea) a certain 'non-locality' that has haunted us to this day. I believe this is also the conceptual source of the "stronger correlations" that Joy interprets in a different fashion. It's complicated, but I believe that reading and rereading pages 7-9 in my essay will help clear it up.
Finally, you ask about "the origin of this wave". It is the gravito-magnetic field ('discovered' by Maxwell and 'built-into' Einstein's relativity field equations). Just as an electric charge moving in an electric field induces electro-magnetic circulation, a mass particle moving in a gravitational field induces gravito-magnetic circulation. It's always there as a physical wave and I show in the essay how and why it corresponds to the probability amplitude.
Thanks for those questions. I hope this helps.
Edwin Eugene Klingman