Is it plausible that the contextuality of meausurements outcomes within distinct contexts is somewhat responsible for the fact that a quantity entity cannot be in two non-orthogonal but complementary/incompatible states at once; or rather cannot be measured sharply along complementary bases; or rather that two noncommuting measurements cannot be jointly conducted.
May it be the case, that this impossibility or fuzziness, leads to might lead to a literal contradiction; that is two orthogonal events of the same observable in the same basis may occur, for some other observable in that context. For example, if observables outcomes cannot have invariant measurement results across all contexts (so that its spin up in certain contexts if its spin down in others); would an attempt to measure any two of the contexts together as part of a joint incompatible context, leads to that same observable being spin up and spin down at the same time. So that complementary is a form of conditional orthogonality;
Are there likewise degrees of complementarity (i hear of notions such as strong complementarity etc) which characterise this as the likelihood of a literal contradiction breaking out in grades, such as necessary, likely, merely possible, thus corresponding to the degrees of fuzziness of the outcomes; and that two bases that are geometrically orthogonal in hilbert space, correspond to this highest degree.
Otherwise what was the reasoning for this non-commutation principle in the first place (presumably it was introduced as a result of the statistical uncertainty and scatter as bounded by heisenbergs inequality) which was confirmed by experiment, but was it derived directly from the formalism.
I presume it also has to with conditional orthogonality of the states of the same basis conditional upon its collapsing into an x eigenstate versus a y one; where inner products of states in say z in these two cases have a zero innerproduct; although what does this correspond to if it is terms of probability; do the relative phases induce correlations so that if one z state gives up, the other z state of the same particle would give down. And otherwise you would have some interference effect (when the inner products are quite zero), corresponding to chance of a contradiction breaking out, if considered to be independent events?;
or merely the fact that this over-determination would alter the probabilities (once one renormalized the event space conditional on the contradiction event not occurring) so that neither wave function state correctly describes the probabilities (and thus considered contradictory in some sense)
(or least an event cannot be in two distinct complementary bases at once, or rather collapse along two bases, at least sharply), or measured simultaneously to give definite results (with probability 1) in both sim
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