I remember reading C. Piron suggesting (in a paper) that his two compatible complement (or orthocomplented) questions corresponding to a questions 'is it 'spin up' 'such that spin up would be the answer giving yes for this question and the other question 'is it spin down' corresponding to the question for which spin down gives an answer yes, cannot be performed simultaneously. Why was this the case?
Is there a connection with the three box paradox; for example can one look in both boxes simultaneously; ie is that one cannot, because if you look in box 1 you get outcome A which is only in one of three boxes, but if you look in box 2 you also get that A is in box 2, so that it would be in both boxes if you look at both; or in this case, can one look at both boxes, and its merely found in one of the two, due to contextual effects.
I believe in speckers seer scenario one can look in all three and only just finds it one of the three boxes, despite the fact that for any two boxes looked at, one finds it one of those two boxes; but is this scenario ruled out in standard quantum mechanics, unlike the three box paradox.
The questions just being an inversion of the eigenvalues of the superpositions of which yes and no correspond, yes in the second question corresponds to orthocomplement of the projection that gave yes in the first question, ie the result that gives no in the first question.
I presume then that he did not mean that this just corresponds merely to placing the detector in a spin up beam versus a spin down beam, as one can place a detector in both.
So that roles of yes- no results are just inverted between the measurement outcomes of the same quantum state state observables's (same basis) measurement outcomes, 'spin up' and 'spin down'. I presume he was not talking about the consideration of totally different basis that the entity was measured in (as these different experiments) unless they corresponded to different quantum contexts, and thus different bases of some other observable which differs between contexts, but not of the particular quantum observable in question.
Thus what did these questions correspond to and what his reasoning for this claim.
I presume his reasoning was the fact that there was always some other question which would give the orthogonal result, so that if the first question gave yes, the second would have also,either due to the observable being in some sense, in an eigenstate of both, (or its eigenstate changes depending on what you ask) so that there are two possible deterministic states, or due to some probabilistic ordering requirement (equiprobable events will receive the same measurement result, yes for spin up question if yes for spin down question (likewise for no results)
LIkewise what does looking at the different boxes correspond to in speckers scenario or in three box paradox,?
(1) basis measurement angle being different for the same two particles (of the three particles, where all three are measured))?, the (2)detectors look at, (3) the detector channel positions, (4) or just which of the two bases (of the three quantum entities) are pre-measured, not distinct angles or bases of the same two entities/boxes/spin particles? I
presume (4) is more likely correct then (1)
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