The discussion centers on the relationship between Positive Operator-Valued Measures (POVMs) and projective measurements in quantum mechanics. Key premises include the necessity of a Hilbert space for both the measured system and the measuring pointer, the existence of associated measures for pointer positions, and the reproducibility of measurement rates through both POVMs and projective measures. The conversation highlights the limitations of using projective measurements to fully encapsulate the advantages of POVMs, particularly in scenarios involving complex measurement interactions.
PREREQUISITESQuantum physicists, researchers in quantum measurement theory, and students studying advanced quantum mechanics concepts will benefit from this discussion.
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.