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Ballentine on the quantum Zeno paradox 
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#1
Nov211, 04:02 AM

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I know that many people here have a very high opinion on the Ballentine's QM textbook. I am also one of them, but one particular subsection of it is (in my opinion) wrong. This is the subsection on the quantum Zeno paradox, or as Ballentine calls it, the "watched pot" paradox in Section 12.2 (Exponential and Nonexponential Decay). In this subsection, he presents a nice standard argument that a continuous observation may prevent decay (which in my opinion is correct), and then in the last paragraph argues that it is false. I think that his argument that it is false  is false itself. What do you think?



#2
Nov211, 05:22 AM

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PF Gold
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I am not sure what "false" means in this context. But the quantum zeno effect is as far as I know routinely observed experimentally. I think it is even used to extend the lifetimes of some states that are used for optical clocks



#3
Nov411, 06:02 AM

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Come on people, so many of you claimed to love this book. Is it possible that nobody has an opinion on this particular subsection?



#4
Nov411, 06:50 AM

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Ballentine on the quantum Zeno paradox
I just looked at it, and I am not sure I understand correctly what he claims. It seems to me that he says that after measuring and finding a value of an observable, the state of system is not the corresponding eigenstate. BUT I thought that this is prat of QM not an interpratation. I suppose I have to read the book first, before commenting. Anyway, why do you think it si wrong.



#5
Nov411, 08:14 AM

PF Gold
P: 3,080

Perhaps you could quote the offending passage? I too feel the Quantum Zeno effect is basic quantum mechanics, so I would like to hear his opinion that it isn't.



#6
Nov411, 10:03 AM

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#7
Nov411, 10:43 AM

PF Gold
P: 1,662

I haven’t read the whole book (yet), so basically I’m just a 'bum', but this is how I see it:
If I was as smart and knowledgeable as Ballentine, and was about to write a QM textbook, I would probably have put it slightly different and hopefully more 'transparent'. But what do I know... 


#8
Nov411, 03:35 PM

PF Gold
P: 3,080

The quantum Zeno effect formally works in the context of discrete eigenvalues, like spin in some direction. I'm not sure how one would apply it to motion, which is normally thought of as a situation where the eigenvalues are continuous. As far as nuclear decay, that isn't thought to be a type of time evolution at all there is no Schroedinger equation that evolves the expectation of nuclear decay, so again I don't see how the Zeno effect would apply there.



#9
Nov511, 12:04 AM

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P: 1,901

1) My first observation is that I suspect the derivation to be faulty, because it takes a limit that corresponds essentially to an infinite tensor product space. This reminds me of what Hartle attempted in his "QM of Individual Systems (1968)" paper, which was subsequently shown to be flawed. See this earlier thread for a bit more detail and references: Ref thread: "Hartle: QM of Individual Systems (1968)" http://www.physicsforums.com/showthread.php?t=511885 (esp. my post #7 at the end). 2) On the experimental "evidence" for the QZ effect, there's also this later paper by Ballentine: L.E.Ballentine, "Comment on Quantum Zeno effect", Phys Rev A., vol 43, no 9, 1991, p5165. Abstract: The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al...], the inhibition of atomic excitation and deexcitation is not due to any "collapse of the wave function", but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as prividing empirical evidence in favor of the notion of "wavefunction collapse". 3) If I'm right in point (1) above, all it means is that Ballentine's "corollary"  i.e., that interpretations of QM can sometimes be experimentally distinguished,  is no longer justified  at least not on this evidence, if the derivation itself is flawed. 


#10
Nov511, 12:07 AM

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#11
Nov511, 01:15 AM

PF Gold
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#12
Nov511, 05:08 AM

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So basically, Ballentine does not believe in the quantum Zeno paradox because he does not believe in collapse.
But it seems that he does not understand that effective collapse can almost be "explained" by modern understanding of decoherence, and it seems to be because he is not aware of the importance of decoherence. The reason for such a suspicion comes from another part of his (otherwise great) book: Sec. 9.3  The Interpretation of a state vector Subsection  The measurement theorem for general states After Eq. (9.13) he writes: "The terms with alpha_r1 notequal alpha _r2 indicate a coherent superposition of macroscopically distinct indicator vectors ... It is clear that the nondiagonal terms in (9.13) cannot vanish ..." But it seems to me that someone who were familiar with decoherence would immediately recognize that they CAN vanish, due to decoherence. Nevertheless, he does not even mention decoherence  at this place at which a "Modern Introduction" to QM should. Any comments? 


#13
Nov511, 07:52 AM

PF Gold
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#14
Nov511, 10:14 AM

P: 592

It does not look like “Ballentine does not believe in the quantum Zeno paradox”, he says “The quantum Zeno effect is not a general characteristic of continuous measurements.” I understand this as follows (and I may be wrong): the quantum Zeno paradox exists or does not exist depending on the specific characteristics of the actual measurement. Furthermore, the authors of the article he (mildly) criticizes write (http://tf.nist.gov/general/pdf/905.pdf ) in the reply to his Comment: “Ballentine states that “collapse of the wave function” is not necessary to quantum mechanics”. We agree. However, we feel that the explanation given in our article, which invokes von Neumann’s “collapse” postulate, is useful for giving a simple explanation of our experiment.” So it looks like there is agreement that collapse is not necessary. You mentioned decoherence. But, as far as I understand, decoherence is a result of influence of environment, i.e. of something external with respect to the experiment, so one can talk about “effective collapse”, but that does not contradict the fact that, strictly speaking, there is no collapse (otherwise unitary evolution is wrong). So I think I fully understand Ballentine’s thrust against collapse. 


#15
Nov511, 10:38 AM

PF Gold
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#16
Nov511, 11:42 AM

P: 476

http://pra.aps.org/abstract/PRA/v41/i5/p2295_1 Maybe Balentine dislikes the quantum zeno effect because is directly related to collapse process in QM, which he rejects, but collapse works http://pra.aps.org/abstract/PRA/v43/i9/p5168_1 


#17
Nov511, 12:09 PM

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#18
Nov511, 12:55 PM

P: 592

Indeed, the text in the book (see, e.g., the quote in kith's post #6 in this thread) gives some grounds to think that Ballentine denies the quantum Zeno effect. It seems to me though that he does not deny the effect, rather he denies its generality. Why do I think so? Because in the quote he refers for details to his article (“Limitations of the Projection Postulate", Found. Phys. 20, 1329–1343 (1990)). He explains in the article that the influence of the detector on the decay rate may indeed all but halt the decay, IF the coupling is strong enough. 


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