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many thanks for very useful and clear answers. I am note yet sure, but i might get back to you via email, if I follow my own question(s) in the directions suggested by your advices.
Regarding many times [‘local time’], which i believe you’re not interested in, just briefly about motivation and the results obtained so far.
Motivation: It’s a natural option within a minimalistic reading of the most basic kinds of physical interactions – in the quantum [many-body] scattering. Another option, of course, is unique time. ‘Minimalistic’ in my use of this word means: ‘add nothing but unavoidable’. As unique time is not unavoidable, we took another, equally valid [and rather intuitively clear] route.
Results: Technically simply reproduces the basic results/conjectures on small (few-body) and large (many particle) systems, routinely describes measurement, resolves the ‘preferred basis problem’ [without invoking ‘collapse’, environmental decoherence or any interpretation–which are required in the unique time QM], and offers a natural interpretation of the Wheeler-DeWitt equation [that is still open in physics of unique time]. And all that without intention–all those have just popped out.