Ben,
Thank you very much for your thoughtful response. As to your historical comments 1 and 4, I certainly agree.
Regarding your point 2 above -- I have no doubt you're right that our current theories need to be modified. But that's beyond my level of competence; the best I can do is to recognize when some brave explorer like yourself has sound instincts about fundamental principles. But, since I do in fact propose looking at SR and QM from a fairly unusual viewpoint, I wanted to emphasize that I'm arguing only from elementary and well-established aspects of current theory, not presuming to offer a new theory of my own.
Regarding 3 -- I don't think any of us are close to understanding "contextuality" sufficiently. Decoherence is surely relevant. As to the Gambini/Pullin essay, I agree with them that we shouldn't be assuming perfectly exact spacetime measurement, and I'm interested in their work on this. However I don't think there's anything to be gained by claiming decoherence solves the measurement problem, as their essay suggests. Most physicists already happily ignore the measurement issue without requiring any such solution in principle. I much prefer Rovelli's approach, which didn't pretend to "solve" the measurement problem but instead tried to make it the basis for a new way of thinking.
The main point I wanted to make about measurement-contexts is (I think) new, although obvious -- namely that measuring any parameter necessarily involves measuring other parameters. To me this means we shouldn't be looking to understand measurement as a single process (e.g. decoherence, or through a theory of objective "collapse"). I think that a universe that can support any kind of observing or communicating of information must have significant structural diversity in its foundations... though we might be able to come up with an evolutionary scenario to show how this sort of functional diversity could emerge from random interaction (see below).
5 -- I apologize for my ignorance on the subject of order theory, but could you please explain to me which partial order is a "refinement" of the other? Is it correct that refinement means adding another set of connections to an existing partial order?
6 -- Your comment makes sense to me, and I too think of Feynman's approach as the one that takes us deepest. As to understanding what an "observer" is, at a fundamental level -- this is indeed difficult. We tend to think of observing and communicating as if they were simple data-transmission processes, ignoring the complicated contexts needed to make data meaningful and empirically definable. If it's true that many different kinds of interaction-contexts are needed to make measurement possible, then we need to ask if there could be simpler "precursors" to what we know as measurement / observation.
For example, suppose we start with completely random interaction, imagined as an infinite randomly connected graph. As a first step toward an observable universe, we could prune off all the vertices that only connect to a single edge, since an isolated interaction can't convey definable information or contribute to a context for defining other information. Whether or not such interactions "exist" in some absolute sense, they remain "virtual" in relation to the remaining graph -- i.e. the vertices that connect other vertices, in a superposition of paths. So far there's nothing like an "individual observer" in the picture.
The next stage might be to distinguish cylic ("self-observing"?) paths from acylic paths. (We might identify the former with all the Feynman-histories that cancel each other out, and so again remain "virtual" relative to the graph of acyclic paths.) Then the question is how to assign directions to the acyclic paths, according to internally-definable rules, that would presumably give us the causal-set structure.
I don't have any clear notion about this, but I have vaguely in mind the way the law of charge-conservation gives us continuous connected paths, and the way charged particles "observe" each other in electromagnetic interaction. There's an intriguing inter-referential structure here relating the spatial direction of the charges' accelerations to the orthogonal E and M components of the field and to the direction of time.
At any rate, the point is that "observing" -- what Rovelli calls "systems having information about other systems" -- may be a combination of many distinct functionalities, some very primitive, defining interaction-structures that provide a basis for the emergence of other more complicated ones. If this conjecture makes any sense, I would imagine the spacetime metric as emerging at quite a high level -- since as I pointed out in my essay, the possibility of measuring intervals in space and time appears to depend on atomic structure, hence on a lot of very finely-tuned physics.
So maybe your "binary relation that generates the causal order" belongs to a quite primitive level of interaction, while your "overall scale factor" that provides "the measure-theoretic information" for the metric may only become definable much later on?
In any case, I very much appreciate your reading the essay and responding so kindly.
Conrad