Ballentine on the quantum Zeno paradox

[Demystifier]

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?

 

[f95toli]

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

 

[Demystifier]

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

 

[martinbn]

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.

 

[Ken G]

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.

 

[kith]

Thus we obtain Pu (t) = 1 (u for the initial undecayed state) in the limit of continuous
observation. Like the old saying “A watched pot never boils,” we have been led to the
conclusion that a continuously observed system never changes its state!

This conclusion is, of course, false. The fallacy clearly results from the
assertion that if an observation indicates no decay, then the state vector must
be |Ψu>. Each successive observation in the sequence would then “reduce” the
state back to its initial value |Ψu>, and in the limit of continuous observation
there could be no change at all. The notion of “reduction of the state vector”
during measurement was criticized and rejected in Sec. 9.3. A more detailed
critical analysis, with several examples, has been given by Ballentine (1990).
Here we see that it is disproven by the simple empirical fact that continuous
observation does not prevent motion. 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.

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.

 

[DevilsAvocado]

... 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?

Maybe he’s both right and wrong?

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 http://pra.aps.org/abstract/PRA/v43/i9/p5165_1" [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! [])
  
  
• 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! ); "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 http://en.wikipedia.org/wiki/Quantum_Zeno_effect#Experiments_and_discussion" 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...

 

[Ken G]

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.

 

[strangerep]

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.

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)"
https://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 "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.

 

[strangerep]

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

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

 

[Ken G]

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.

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.

 

[Demystifier]

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?

 

[DevilsAvocado]

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

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"!

 

[akhmeteli]

So basically, Ballentine does not believe in the quantum Zeno paradox because he does not believe in collapse.

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 (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.

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?

I cannot be sure Ballentine knew about decoherence in 1998, when his book was published (he knew about it in 2005 though :-) - http://pra.aps.org/abstract/PRA/v72/i2/e022109 ), 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 https://www.physicsforums.com/showpost.php?p=2534950&postcount=41 ).

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.

 

[DevilsAvocado]

I don’t have the Ballentine’s book

http://www.google.com/search?hl=en&q=quantum+mechanics+a+modern+development+pdf"

 

[juanrga]

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?

Best known as Quantum Zeno effect, which has been measured

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

 

[juanrga]

I cannot be sure Ballentine knew about decoherence in 1998, when his book was published (he knew about it in 2005 though :-) - http://pra.aps.org/abstract/PRA/v72/i2/e022109 ), 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.

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.

 

[akhmeteli]

http://www.google.com/search?hl=en&q=quantum+mechanics+a+modern+development+pdf"

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.

 

[akhmeteli]

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

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."

 

[akhmeteli]

Sorry to remark the obvious but that is known since von Neumann introduced the collapse postulate in QM.

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" :-)

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.

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.

 

[akhmeteli]

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?

Now that I have looked at the text :-), Ballentine does mention decoherence, although not by name:

"Some of the proposed explanations [of collapse] are as follows:...

(iii) The reduction (9.9) is caused by the environment, the “environment” being defined as the rest of the universe other than [the object] (I) and [the apparatus] (II).

This proposal is a bit vague, because it has not been made clear just what part of the environment is supposed to be essential. But it is apparent that if we formally include in (II) all those parts of the environment whose influence might not be negligible, then the same argument that defeated (i) and (ii) will also defeat (iii)."

 

[unusualname]

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?

Good point, and in fact, Ballentine is notorious for downplaying (or not understanding) the role of decoherence. In 2005 he published an attempted rebuttal (The Quantum Mechanics of Hyperion) of an argument by Zurek (Why We Don't Need Quantum Planetary Dynamics: Decoherence and the Correspondence Principle for Chaotic Systems), the argument was resolved, in Zurek's favour, by Schlosshauer (Classicality, the ensemble interpretation, and decoherence: Resolving the Hyperion dispute)

 

[juanrga]

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

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."

In that paper they are replying invalid statements done by Ballentine about their work.

The collapse is needed for any consistent formulation of QM. That is why standard textbooks use it.

 

[juanrga]

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.

But Ballentine's is not a standard textbook in QM. It is a textbook about how he want QM to be.

Schlosshauer, could be replied with there is no positive experimental evidence of unitarity for the universe as a whole.

 

[akhmeteli]

In that paper they are replying invalid statements done by Ballentine about their work.

I have no comments on this statement as it does not seem to contain any specifics relevant to this thread.

The collapse is needed for any consistent formulation of QM.

Again, seems like the authors of your source agree with the opposite point of view.

Furthermore, as soon as any interpretation includes both unitary evolution and collapse, strictly speaking, it becomes inconsistent, as these two are mutually contradictory.

 

[akhmeteli]

But Ballentine's is not a standard textbook in QM. It is a textbook about how he want QM to be.

What criteria do you use to declare Ballentine's book non-standard? The fact that he rejects collapse?

Schlosshauer, could be replied with there is no positive experimental evidence of unitarity for the universe as a whole.

OK, so you believe we need collapse. I believe we need unitary evolution and therefore I cannot accept collapse.

 

[Len M]

The collapse is needed for any consistent formulation of QM. That is why standard textbooks use it.

From my reading of Bernard d'Espagnat (who has written extensively on the conceptual foundations of quantum mechanics), he doesn’t seem to consider the collapse to be a fundamental requirement for consistency within QM. I can’t offer any more than that, so I’m really just quoting d’Espagnat parrot fashion, but the fact that he does make a point in specifying that waveform collapse is “never absolutely necessary” with no mention of the shortfall in consistency you mention, then perhaps it’s not as clear cut as you imply. What he seems to imply is that it is a “useful” concept, not an “essential” concept.

From Bernard d’Espagnat, “On Physics and philosophy”.

Finally, concerning the quantum rules let us note that, within the convention taken up in this book, the set of them all does include the (generalized) Born rule (which yields probabilities of observation on the basis of knowledge of the wave function) but does not include the (already alluded to ) procedure called “reduction” or “collapse” of the wavefunction. The point is worth mentioning since, in many texts, the two procedures are described together and are not clearly distinguished. In fact, while the latter is often extremely useful, in theory it never is absolutely necessary.

 

[juanrga]

Again, seems like the authors of your source agree with the opposite point of view.

My 'source' was the phrase immediately posterior and that you deleted. The authors of that paper also say that Everett interpretation of QM is acceptable, but that is far from true. Everett work is wrong (even well-known many-world believers accept that now) and discussion of the mistakes and inconsistencies of «many-worlds» was given in another recent thread.

That paper was cited because replies a series of incorrect statements done by Ballentine in his «comment on».

Furthermore, as soon as any interpretation includes both unitary evolution and collapse, strictly speaking, it becomes inconsistent, as these two are mutually contradictory.

No inconsistency, because it is done clear that each postulate describes a type of evolution and not the other. Did not you read von Neumann?

The correct term is incompleteness, because the postulates by themselves cannot really say what is exactly the limit of validity of each.

Those limits are however, well understood using generalizations of QM, as the ones based in Stochastic Schrödinger equations or further generalizations.

 

[akhmeteli]

My 'source' was the phrase immediately posterior and that you deleted.

I deleted it just because the phrase was repeated elsewhere, and I did not want to give a response to the phrase twice. My response was that not all standard textbooks use collapse, and when you said that Ballentine’s textbook is non-standard, I asked you what criteria you use, and I still wonder what those criteria might be.

The authors of that paper also say that Everett interpretation of QM is acceptable, but that is far from true. Everett work is wrong (even well-known many-world believers accept that now) and discussion of the mistakes and inconsistencies of «many-worlds» was given in another recent thread.

You may reject Everett, I also reject Everett, but I believe “many-worlds” is still one of mainstream interpretations, no matter what was written “in another recent thread”, so what the authors say does not mean they are off-mainstream. I have no intention to defend many-worlds though.

That paper was cited because replies a series of incorrect statements done by Ballentine in his «comment on».

Again, without any specifics, I am not sure this is relevant.

No inconsistency, because it is done clear that each postulate describes a type of evolution and not the other. Did not you read von Neumann?

As a matter of fact, I did read von Neumann.
So there is no inconsistency? Congratulations! Looks like you have just solved the problem of measurement in quantum theory!
I insist though that there is no positive evidence of non-unitary evolution. On the other hand, you can consider unitary evolution of the system that, in your opinion, should be described by non-unitary evolution (including the instrument and, if you wish, the observer, in such a system). The results of the two evolutions are mutually contradictory. Any reason why unitary evolution is not appropriate for such a system?

The correct term is incompleteness, because the postulates by themselves cannot really say what is exactly the limit of validity of each.

Those limits are however, well understood using generalizations of QM, as the ones based in Stochastic Schrödinger equations or further generalizations.

This seems to suggest that you admit that the projection postulate has some limits of validity. But it seems I am saying pretty much the same: the projection postulate may be a good approximation, but it’s just an approximation. On the other hand, in my opinion, unitary evolution never “calls in sick”.

 

[Runner 1]

But Ballentine's is not a standard textbook in QM. It is a textbook about how he want QM to be.

His book has far less errors than most textbooks describing quantum mechanics. I don't understand -- why is it non-standard? A professor can use whatever textbook he wishes to teach the class.