Dear Alan,
I just read your essay and I have some serious questions:
1) Does the background vector field define a preferred rest frame?
Since your framework is explicitly relativistic, the answer would have to be be no, but then I have difficulty seeing how the frame in which the rotators are all at rest is not preferred over all others. Indeed I come away with the impression that in your framework, motion (other than that associated with the rotators) is an illusion and that everything is really at rest, but just "pops" in and out so to make it appear as if it is moving in space.
2) Do the rotators define a preferred plane orientation in space?
It seems that you would want the answer to be "no" for otherwise isotropy of space is broken with concomitant consequences for angular momentum conservation. But then I have a difficulty visualizing the rotator. Is the plane of the rotator relative to the observer? What if you have multiple observers observing an object from different angles? Do you have multiple rotators at the same location but rotating along different directions? This is very fuzzy to me.
3) What does the amplitude of the rotator signify?
I missed a physical interpretation of the rotator, and related to this question is whether it is possible to define a rotator density. Is this possible and if so, how does it relate to the amplitude?
4) How do you get the Born Rule out of the framework for elementary and composite particles such that it takes the differences in your framework into account?
You mentioned the Born Rule in your essay but then went right on to other aspects of QM, so that I am not at all clear how you get the Born Rule out of your framework.
5) Do the rotators only rotate in one direction?
As you know, from the Born rule one can deduce that the complex conjugate of the quantum state is physically on the same footing as the state itself. How do you account for that in your theory? Also, I am not sure on this but it seems to me that if you have two observers between whom the rotator field that describes a particle is located, they would have to give opposite descriptions of the rotational direction.
6) How does your framework account for contextuality?
If the spin values of elementary particles are already determined before a measurement, then this would seem to violate Kochen Specker, or the simpler analogues like the Mermin magic square. How do you avoid this?
7) Why should nature be characterized just in the way by the model you describe as opposed to some other?
I guess this is more of a metaphysical question, and I should admit that I have a philosophical prejudice that at bottom nature is fundamentally simple and intelligible to us. Your model may unify some aspects of nature that are currently not describable in a unified way, but frankly it seems no more intuitive or conceptually intelligible than quantum mechanics to me. The questions that come to my mind are: Why rotators? What are they made of? Why a particular frequency or amplitude that characterizes each (as opposed to a distribution)? Can an individual rotator be isolated?
There are also a few statements that I think will be regarded as controversial by some physicists:
"In the orthodox Copenhagen
interpretation, the quantum wave is instead a statistical distribution of point particles"
My understanding is that the orthodox Copenhagen interpretation only regards post-measurement states as point particles. If it is characterizable as a quantum wave, it is a pre-measurement state.
"Similar Hilbert space product states provide the basis for quantum entanglement, whereby a measurement on one particle in a pair of coupled particles immediately changes the physical state of the other particle"
I think that this statement is stronger than what has been experimentally shown, and though some physicists do believe that this is what entanglement amounts to, I think it is a misunderstanding.
All the experiments license us to claim is that if we perform a set of measurements on spacelike separated entangled states we will, after we bring the measurement results together, notice that they were correlated with each other.
The difference between your statement and mine is subtle but real. To see this consider just that in SR the time ordering for spacelike separated events is frame-dependent. Your statement can then only be true if there was an absolute frame in which one measurement event came before the other, or if retroactive causal effects are admitted, both highly dubious. But instead of thinking that this means that standard QM is wrong, I think it is better to just stick to what the experiment licenses us to claim: If A performs a measurement on a, she is only entitled to claim that if B makes a measurement on b, he will find a correlated result. This does not imply that A's measurement of a changed the state of b before B's measurement of b (your statement).
The difference is that B still needs to perform a measurement in order to establish the correlation whereas your statement implies that this is unnecessary. In my view, the necessity that B needs to make a measurement is quite consistent with the orthodox view that in essence, the observer "creates" the particle with a measurement. Before B makes a measurement *there is no particle* which subsumes the fact that there is no correlated particle.
Of course, this does not answer the question of how the correlations are enforced for spacelike separated events. This is regarded as an open question, but I'd like to mention that I just gave a talk on this where at least it seems to me that the framework on which I have been working on suggests a simple answer, and the talk slides (a quick read) are available online:
http://vixra.org/pdf/1306.0097v2.pdf
Lastly, allow me to state that I found your essay very clearly written. I think that answering the questions above will go a long way toward persuading others of the merits of your idea.
All the best,
Armin