Thanks for your clearly stated question, I think you've located the thing that's troubling me.
I've been trying to suggest that two propositions are inconsistent:
(i) Schrodinger evolution rotates the state vector continuously.
(ii) It is possible for Schrodinger's cat to simply die...
Not if by "quantum jump" you mean wave-function collapse or state reduction. I'm here only considering purely unitary linear Schrodinger dynamics.
That makes it sound like you're considering the dynamics of an open microsystem in a heat bath or something. But I'm considering the dynamics of...
Thanks. This is getting to the issue...
It's slightly more than the fact that U(t) preserves the norm i.e. only changes the direction but never the unit-length of the state vector. I'm also assuming that U(t) never induces sudden jumps regarding the direction it points to, so there are only...
Are you trying to say that going from:
a|Alive>|decay>+b|Alive>|~decay>
to:
a|Dead>|decay>+b|Alive'>|~decay>
involves a mere infinitesimal rotation of the state vector, within the vector space with basis vectors that include: |Alive>|decay> and |Alive>|~decay> and |Dead>|decay> and...
You're absolutely right that a more precise statement of Schrodinger's paradox would account for the fact that e.g. the cat is shedding fur etc. But how does that help? It seems my question still remains even when we account for this by stating the evolution as:
[t1] |Alive>|contained>(a|decay>...
No I am not asking about wave function collapse. In fact the whole point of Schrodinger's thought experiment is to show what happens (a) when you correlate the state of a macro-system to the quantum state of a particle and (b) when collapse NEVER occurs, i.e. when the dynamics is given...
The Schrödinger equation rotates the state vector in Hilbert space continuously (i.e. without jumps). This makes sense for individual systems, but I'm finding this hard to reconcile with coupling or entanglement. For example, consider how Schrödinger's cat paradox is typically presented (in...
Well I just found a very nice paper on this:
http://www.phys.lsu.edu/~amarti9/adfaerf/288.%20Quantum%20Zeno%20and%20anti-Zeno%20Effects%20An%20Exact%20Model.pdf
My mathematical background isn't yet sufficient to fully understand this. Nonetheless, it seems that you're right that continuous...
Okay so for open or closed systems, perfectly continuous measurement yields QZE, moreover closed plus merely frequent measurement yields (approximate) QZE, ...but open plus merely frequent measurement yields QAZE? Or are the conditions less general than this?
Actually http://dml.riken.jp/pub/nori/pdf/Srep01752.pdfis slightly more clear:
"In the quantum Zeno effect (QZE) frequent measurements inhibit atomic transitions for a
closed system. In the quantum anti-Zeno effect (QAZE), atomic decays can be accelerated by frequent measurements, when the...
Hmm that's interesting. Going through the literature I've not found anyone saying that it's to do with the rate of the measurements. Rather, it appears to have something to do with what's being measured. So for example, here it is claimed that it is "near threshold decay processes" that may be...
With the help of some kind PF folk I recently comprehended the idea of the quantum zeno effect. The idea now seems reasonably simple - the survival probability for any given quantum state tends to one as measurements of that state tend to infinity (over a given time), as a mathematical...
No no, that's its exact intention. The authors just don't agree with your claim about the two axioms being all there is to it. I don't see any point continuing this if you're just going to dismiss such views as nonsense.
Take care.
JMC