Ballentine on the quantum Zeno paradox

  1. Demystifier

    Demystifier 5,594
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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. jcsd
  3. f95toli

    f95toli 2,472
    Science Advisor
    Gold Member

    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
  4. Demystifier

    Demystifier 5,594
    Science Advisor

    Come on people, so many of you claimed to love this book. Is it possible that nobody has an opinion on this particular subsection?
  5. 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.
  6. Ken G

    Ken G 3,618
    Gold Member

    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.
  7. kith

    kith 946
    Science Advisor

    I don't think this is an empirical fact. My current knowledge is, that decays have been successfully suppressed as predicted by the quantum zeno effect. Although I'm not familiar with recent experiments, I don't see how real "continuous" measurements could be performed at all.
  8. DevilsAvocado

    DevilsAvocado 1,665
    Gold Member

    Maybe he’s both right and wrong? :rolleyes:

    I haven’t read the whole book (yet), so basically I’m just a 'bum', but this is how I see it:
    • Yes, not only in the textbook has Ballentine been advocating this approach, but also in the paper Comment on ‘‘Quantum Zeno effect’’ [Phys. Rev. A 43, 5165–5167 (1991)]; "The quantum Zeno effect is not a general characteristic of continuous measurements".

    • Ballentine is a prominent advocate of the Ensemble interpretation. (And here I just know he’s dead wrong! :grumpy: [:smile:])

    • Ballentine seems to use the refutation of the "watched pot"/"Zeno effect" as some form of 'evidence' for a 'particular' interpretation (and we all know which! :smile:); "It is sometimes claimed that the rival interpretations of quantum mechanics differ only in philosophy, and cannot be experimentally distinguished. That claim is not always true, as this example proves". To me, this is wrong. If a QM interpretation makes different predictions than 'the others', then it’s no longer an interpretation, but a new theory.

    • According to Wikipedia, the Quantum Zeno Effect is still an open question when it comes to the limit of an infinite number of interrogations; "It is still an open question how closely one can approach the limit of an infinite number of interrogations due to the Heisenberg uncertainty involved in shorter measurement times. ... The interpretation of experiments in terms of the "Zeno effect" helps describe the origin of a phenomenon. Nevertheless, such an interpretation does not bring any principally new features not described with the Schrödinger equation of the quantum system". Here it looks like Ballentine has a point.

    • And this point becomes his main argument (afaict); "We now pass to the limit of continuous observation by letting n become infinite".

    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... :rolleyes:
  9. Ken G

    Ken G 3,618
    Gold Member

    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.
  10. strangerep

    strangerep 2,292
    Science Advisor

    I read that section years ago, and have just now studied it again. I offer the following thoughts...

    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)"
    (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.


    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 "wave-function 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.
  11. strangerep

    strangerep 2,292
    Science Advisor

    Unless you have experimental evidence that can distinguish between interpretations, you only believe he's "dead wrong".
  12. Ken G

    Ken G 3,618
    Gold Member

    Hmm, so a strong perturbation in the process of doing a measurement is not a collapse of the wavefunction? It sounds like one of the more blatant examples of collapse of a wavefunction.
  13. Demystifier

    Demystifier 5,594
    Science Advisor

    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?
  14. DevilsAvocado

    DevilsAvocado 1,665
    Gold Member

    Okay, fair enough (if we pretend not to understand the meaning of a smiley), but as I see it, there must be a flip side to the coin; Ballentine only believe he's "dead right"! :tongue:
  15. I don’t have the Ballentine’s book (and Ballentine’s no relative of mine :-) ), so the following is mostly based on his Comment quoted by DevilsAvocado in post 7 in this thread.

    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 ( ) 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.

    I cannot be sure Ballentine knew about decoherence in 1998, when his book was published (he knew about it in 2005 though :-) - ), but in the text you quoted he seems to argue that collapse is, strictly speaking, incompatible with unitary evolution, and I believe he’s right. Furthermore, it seems there is no positive experimental evidence of collapse (see the quote from Schlosshauer’s article at ).

    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.
  16. DevilsAvocado

    DevilsAvocado 1,665
    Gold Member

  17. Best known as Quantum Zeno effect, which has been measured

    Maybe Balentine dislikes the quantum zeno effect because is directly related to collapse process in QM, which he rejects, but collapse works
    Last edited: Nov 5, 2011
  18. Sorry to remark the obvious but that is known since von Neumann introduced the collapse postulate in QM. As any standard textbook in QM explains there are two evolutions in QM: (1) the unitary described by the Schrödinger equation and (2) the non-unitary described by the collapse postulate.
    Last edited: Nov 5, 2011
  19. Thank you.

    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.
  20. Collapse may be a good approximation and work in some situations, but again, the authors of the source you quote agree that ""collapse of the wave function" is not necessary to quantum mechanics."
  21. I agree. The problem is many people do agree that "collapse is, strictly speaking, incompatible with unitary evolution", but immediately add: "but that's OK" :-)

    Except that the "standard textbook in QM" that we are discussing rejects the postulate of collapse:-) Let me repeat that, say, according to Schlosshauer, there is no positive experimental evidence of collapse.
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