Hello, Given a system and an observable that one wants to measure in it, how does on get the (or a?) relevant hilbert space and the suitable operator in it? The examples I've come across so far seem to rely on... well, I'd call it "vague reasoning", but the word 'reasoning' seems too much. It seems like the idea is "well we're just guessing and then predict some things and it turns out that they're experimentally verified", so I was wondering if there's a more elegant way to determine them? On a related note, what constitutes a measurement as corresponding to an operator? Apparently something called "weak measurement" is not allowed, which is basically (for example) inference about momentum based on a position measurement. That's okay, I suppose, neglecting that kind of measurement, but then I expect, in return, a clear definition of what is considered as a "valid" measurement. Or can it not be given and is it left intentionally vague? To try and start the concrete specification of a "valid" measurement, I might suggest the following: "it" has to happen on a specific time t (?).