- #31
Fra
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These are interesting questions, which can either be both of mathematical foundation interest or interest to those trying to understand the conceptual foundations of QM, not sure where you come from.
From the conceptual perspective I think the of significance of the distance metrics in the abstrac spaces as beeing (not equal to but) related to what one may call "a priori transition probabilites". The the bures measures measure, beeing a generalisation from the hilbert metric to one on density operators, is related to fidelty which is associated to transition probabilities. https://arxiv.org/abs/1106.0979
But It seem your question was something else, if this "distance" has an meaning in the "interference", and if the "interference" has a process or more a logical consequence.
The way I interpret your thinking, I would prefer to think of "quantum interference" first of all as a logical consequence of how the initial conditions, where we "know" values of non-commuting observables. But that doesn't mean it's "instant" whatever happens, has some dynamics, but the "phenomeman" of quantum interference i view as a logical consequence. To question further would mean to ask "why" does systems seem to exist in stable states specified by non-commuting information. This gets interpretational I think.
I do not see a clear connection between the a priori the transition probabilities between two states and their interference, as I think interference is between PARTS of ONE system, not between two different hypothetical states that don't exist at the same time?
Not sure if I missed your point
/Fredrik
From the conceptual perspective I think the of significance of the distance metrics in the abstrac spaces as beeing (not equal to but) related to what one may call "a priori transition probabilites". The the bures measures measure, beeing a generalisation from the hilbert metric to one on density operators, is related to fidelty which is associated to transition probabilities. https://arxiv.org/abs/1106.0979
But It seem your question was something else, if this "distance" has an meaning in the "interference", and if the "interference" has a process or more a logical consequence.
The way I interpret your thinking, I would prefer to think of "quantum interference" first of all as a logical consequence of how the initial conditions, where we "know" values of non-commuting observables. But that doesn't mean it's "instant" whatever happens, has some dynamics, but the "phenomeman" of quantum interference i view as a logical consequence. To question further would mean to ask "why" does systems seem to exist in stable states specified by non-commuting information. This gets interpretational I think.
I do not see a clear connection between the a priori the transition probabilities between two states and their interference, as I think interference is between PARTS of ONE system, not between two different hypothetical states that don't exist at the same time?
Not sure if I missed your point
/Fredrik