Alan
Frank cited my essay above in context with the soliton. But I find greater consistency with yours as the only other essay so far (I've read) to recognise and explain the importance of the detector as part of the process.
I go on to explore a real ontological construction, with exciting results, but find only a simple mathematical description (see my end notes) of various relative kinetic cases.
Long ago I found issues with maths and geometry. Motion is an invalid concept in geometry and I particularly challenged it's validity in algebraic vector space, where the word 'frame' is assumed as a 'wire frame' which can overlap with other in Cartesian systems. Using non point particles interacting, including with just waves, over non zero time resolves this. Space-time is indeed then 'granular'.
In constructing the ontology with logic I can't express it mathematically, but am sure you can. In particular the nested mutually exclusive structure of truth propositional logic applies, along with an interpretation of the 'interleaved' modes of Propositional Dynamic Logic. (Each representing a discrete and equivalent 'Space time geometry'). Enough of mine but please do read, analyse (beneath the theatrical metaphors) and comment.
I find the heart of yours in the paragraphs;
"If the solution were known exactly at some instant before the interaction then a numerical calculation could reveal the free space states which the detectors would converge to afterwards. However, uncertainty is inevitable because we, our memories, and any possible measuring apparatus are part of the solution. No solution is capable of discovering and internally representing what it itself is.
...In every free space solution for a detector, either the detector has detected the quantum or it has not. After diffraction, the solution almost certainly converges to just one such set of overlapping free space solution because any other solution would be unstable."
Please expect a top score from me if only for that. You should find my real local nature equivalent, and I'm quite convinced by the vast evidence I have beyond the essay that we have the key to the toe. (Many others here are also consistent).
Very best wishes.
Peter
