The discussion revolves around the relationship between Positive Operator-Valued Measures (POVMs) and projective measurements in quantum mechanics. Participants explore whether POVM measurements can be explained through projective measurements, considering theoretical implications, mathematical formulations, and the nature of measurement in quantum systems.
Participants do not reach a consensus on whether POVM measurements can be fully explained by projective measurements. Multiple competing views remain regarding the implications and interpretations of both measurement types.
Participants note that the discussion is limited by assumptions about the nature of measurements and the mathematical frameworks employed, particularly regarding the implications of discrete versus continuous eigenvalues and the role of consistent histories.
Eq. (18) and the text before it. More details in the link in post #24.A. Neumaier said:where?
This is not a construction but a sketchy outline of a program that to make it work one would have to justify by a serious derivation.Demystifier said:Eq. (18) and the text before it. More details in the link in post #24.
I'm not sure I understand your point. Are you saying that in the literature only the non-demolition is assumed, while I assume something additional? What is this additional assumption that I make?A. Neumaier said:Instead you make strong assumptions about arbitrary measurements that go far beyond what has been demonstrated in the literature (where always a nondemolition assumption was involved to get decoherence).
No. You make fewer assumptions but pretend that essentially the same results follow, without telling why this should be so.Demystifier said:I'm not sure I understand your point. Are you saying that in the literature only the non-demolition is assumed, while I assume something additional? What is this additional assumption that I make?
I make fewer explicit assumptions, but the assumptions are implicitly there. That's because I think like physicist, not mathematician, so I try to explain how nature works, not to present a mathematical proof. I don't make explicit assumptions which seem obvious to me from a physical point of view, because I see such details as distraction from really important ideas. But I perfectly understand that you, as a mathematician, don't like this type of reasoning.A. Neumaier said:No. You make fewer assumptions but pretend that essentially the same results follow, without telling why this should be so.
I am not requiring mathematical rigor. But physics has a long and successful tradition in giving proofs at a high level, a level missing in your paper. You make suggestions, which might motivate why the results could possibly be true, but fail to give arguments that would satisfy anyone who really wants to understand what is behind. Your references to the literature only cover conditions where much stronger assumptions are needed to actually make a convincing justification.Demystifier said:I make fewer explicit assumptions, but the assumptions are implicitly there. That's because I think like physicist, not mathematician, so I try to explain how nature works, not to present a mathematical proof. I don't make explicit assumptions which seem obvious to me from a physical point of view, because I see such details as distraction from really important ideas. But I perfectly understand that you, as a mathematician, don't like this type of reasoning.