Errors in Ballentine (QM Textbook)?

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Summary:

Asking for specific examples of claimed errors in the QM textbook by Ballentine.
This thread is to get more specifics and start discussion regarding two recent claims in other QM forum threads, in a separate thread to avoid clutter in other discussions:

Ballentine lacks a clear statement of collapse or state reduction. He misrepresents the Copenhagen interpretation, and suggests that the Copenhagen interpretation is in conflict with experiment (Chapter 9). Ballentine's lack of collapse makes him give the wrong result in conflict with experimental outcomes on the "watched pot" experiment.
I think Ballentine is plain wrong on fundamentals
@atyy, can you give specific quotes and references (chapter/page) in Ballentine that these quotes are talking about?
 
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  • #2
atyy
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Section 9.5 on the spin recombination - here Ballentine suggests that experimental evidence contradicts Copenhagen (whereas it only contradicts his misunderstanding of Copenhagen)
"Some evidence that the state vector retains its integrity, and is not subject to any “reduction” process, is provided by the spin recombination experiments that are possible with the single crystal neutron interferometer (see Sec. 5.5)."

Ballentine's errors on the watched pot experiment have been discussed in https://www.physicsforums.com/threads/ballentine-on-the-quantum-zeno-paradox.546523/

Ballentine's famous review from the 1970s also has errors, where he suggests that position and momentum can be simultaneous measured. While there are special cases, in general his language is misleading, because he gives an example in Fig 3 in which the variables are not canonically conjugate. In his review he makes it clear he is attacking the "orthodox" interpretation.

Of course errors do not make a textbook bad - the wonderful Feynman lectures have errors - some deep (though at that time they were not widely well understood), some incidental - but Ballentine attacks mainstream quantum mechanics, and substitutes his own personal theory.
 
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  • #3
martinbn
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The watched pot is at the end of 12.2, page 432 of the 1998 edition.
 
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Delta2
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I am interested in buying Ballentine since it is recommended by @PeterDonis but let me ask something.

I don't care that much if Ballentine has his own variation of Copenhagen interpretation, but how to say it, is the book proper for someone that wants to learn QM from the complete unknown (ok I have heard Schrodinger equation before i am not that dumb), is it taught at the undergraduate level? Or Ballentine goes wild (as like say Jackson goes wild in Classical Electrodynamics where he states as obvious, things that their derivation is three pages long).

I have finished my undergraduate studies in math long ago (back at 1998) and during those I had taken an optional course in QM that was offered. The textbook was in Greek i still have it but I don't think it is so good.
I didn't bother with QM since then.

I searched for the book at amazon, which one of these is the first or the second?
Amazon.com : ballentine quantum mechanics
 
  • #5
atyy
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I don't care that much if Ballentine has his own variation of Copenhagen interpretation, but how to say it, is the book proper for someone that wants to learn QM from the complete unknown (ok I have heard Schrodinger equation before i am not that dumb), is it taught at the undergraduate level? Or Ballentine goes wild (as like say Jackson goes wild in Classical Electrodynamics where he states as obvious, things that their derivation is three pages long).
I don't think Ballentine has his own variation of Copenhagen - I think it is simply wrong - you can find the orthodox interpretation in many textbooks - Dirac; Landau & Lishitz; Messiah; Weinberg; Cohen-Tannouji, Diu & Laloe; Shankar; Griffiths; Gasiorowicz; Nielsen & Chuang - Ballentine is not in step with them, and you may be taken in by his errors if you don't start with sound foundations.
 
  • #6
martinbn
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I am interested in buying Ballentine since it is recommended by @PeterDonis but let me ask something.

I don't care that much if Ballentine has his own variation of Copenhagen interpretation, but how to say it, is the book proper for someone that wants to learn QM from the complete unknown (ok I have heard Schrodinger equation before i am not that dumb), is it taught at the undergraduate level? Or Ballentine goes wild (as like say Jackson goes wild in Classical Electrodynamics where he states as obvious, things that their derivation is three pages long).

I have finished my undergraduate studies in math long ago (back at 1998) and during those I had taken an optional course in QM that was offered. The textbook was in Greek i still have it but I don't think it is so good.
I didn't bother with QM since then.

I searched for the book at amazon, which one of these is the first or the second?
Amazon.com : ballentine quantum mechanics
I would say that the level is graduate or advanced undergraduate, but i might be wrong. It just means that it may be that you need to put in more effort compare to other texts, but in my opinion you will benefit more. As to the "errors" discussed here, they are less than 1% of the book, so you will not even notice them.
 
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  • #7
Demystifier
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is the book proper for someone that wants to learn QM from the complete unknown (ok I have heard Schrodinger equation before i am not that dumb), is it taught at the undergraduate level? Or Ballentine goes wild (as like say Jackson goes wild in Classical Electrodynamics where he states as obvious, things that their derivation is three pages long).
I would agree with @martinbn that Ballentine is an advanced book, very much like Jackson for electrodynamics.
 
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  • #8
Demystifier
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I don't think Ballentine has his own variation of Copenhagen - I think it is simply wrong - you can find the orthodox interpretation in many textbooks - Dirac; Landau & Lishitz; Messiah; Weinberg; Cohen-Tannouji, Diu & Laloe; Shankar; Griffiths; Gasiorowicz; Nielsen & Chuang - Ballentine is not in step with them, and you may be taken in by his errors if you don't start with sound foundations.
Paradoxically, even though those other books do not make the fundamental error that Ballentine does, one can learn foundations much more deeply from Ballentine than from those other books. That's because Ballentine takes much more space and effort than the other books to discuss foundations at a deep level, while other books are rather superficial on that. It's much easier to make an error if you try to think deeply than if you choose to stay in the safety zone.
 
  • #10
atyy
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Paradoxically, even though those other books do not make the fundamental error that Ballentine does, one can learn foundations much more deeply from Ballentine than from those other books. That's because Ballentine takes much more space and effort than the other books to discuss foundations at a deep level, while other books are rather superficial on that. It's much easier to make an error if you try to think deeply than if you choose to stay in the safety zone.
I can't agree. Copenhagen is what makes the measurement problem clear. And the measurement problem is the fundamental problem in foundations. I think it is telling that Ballentine does not give the merits of the Bohmian interpretation clearly, instead favoring his own non-solution of the Ensemble Interpretation (which is just Copenhagen without the proper postulates), because Ballentine is unaware that there is a measurement problem.

Ballentine's Ensemble Interpretation is not Einstein's ensemble intrepretation, because it lacks a clear statement of hidden variables. In contrast the old books like L&L allude pretty clearly to an absurdity, and Messiah explicitly discusses Einstein's proposal of hidden variables.
 
  • #11
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I can't agree. Copenhagen is what makes the measurement problem clear. And the measurement problem is the fundamental problem in foundations. I think it is telling that Ballentine does not give the merits of the Bohmian interpretation clearly, instead favoring his own non-solution of the Ensemble Interpretation (which is just Copenhagen without the proper postulates), because Ballentine is unaware that there is a measurement problem.

Ballentine's Ensemble Interpretation is not Einstein's ensemble intrepretation, because it lacks a clear statement of hidden variables. In contrast the old books like L&L allude pretty clearly to an absurdity, and Messiah explicitly discusses Einstein's proposal of hidden variables.
Yes, but I think Ballentine is great on other foundational problems that are not directly related to the measurement problem.

Even his errors are instructive, because they are presented in a form that provokes thinking. :oldbiggrin:
 
  • #12
PeterDonis
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Section 9.5 on the spin recombination - here Ballentine suggests that experimental evidence contradicts Copenhagen (whereas it only contradicts his misunderstanding of Copenhagen)
The term "Copenhagen" never appears in that section, so I don't see how Ballentine is claiming that experimental evidence contradicts "Copenhagen". I do think it is true that in that section, Ballentine is using the term "reduction" in an idiosyncratic way, driven by his preference for the ensemble interpretation. However, since this thread is not in the QM interpretation forum, I don't want to get into detail here about how Ballentine deals with QM interpretation/foundations issues vs. other sources--if there is enough interest for that type of discussion I can spin off a separate thread in the interpretations/foundations subforum.

Ballentine's errors on the watched pot experiment
Hm, yes, I agree that his argument at the end of the "watched pot" subsection of 12.2 is just handwaving: no math and no explanation, just a bare assertion.

Ballentine attacks mainstream quantum mechanics, and substitutes his own personal theory.
I think this is too strong (as is the claim that Ballentine is "plain wrong on fundamentals"). To the extent Ballentine differs from other sources with regard to which interpretation of QM he prefers, and points out issues he sees with other interpretations, that is not "personal theory" unless every QM textbook that discusses interpretation at all is "personal theory". The fact is that there are multiple interpretations of QM, and with our current state of knowledge, none of them are "wrong" (or "right", for that matter). I think a better description of this aspect (and, as noted above, if more detailed discussion is desired I can spin off a separate thread in the appropriate subforum for that) would be that Ballentine's preferred interpretation is not shared by most other sources, and that one should not use his textbook as one's only source of information about interpretations.

I do agree that all that makes his textbook an "advanced" one, as has been commented, and after seeing this discussion I would be much more hesitant about recommending it to someone with no prior background in QM, unless that person is also learning from other sources.
 
  • #13
PeterDonis
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is the book proper for someone that wants to learn QM from the complete unknown
Per my post #12 just now, I would be hesitant about this if it's going to be your only source, particularly about QM interpretations.

I do think there is a lot of useful information in Ballentine, and also good problems in the problem sections at the end of each chapter.
 
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  • #14
atyy
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The term "Copenhagen" never appears in that section, so I don't see how Ballentine is claiming that experimental evidence contradicts "Copenhagen". I do think it is true that in that section, Ballentine is using the term "reduction" in an idiosyncratic way, driven by his preference for the ensemble interpretation. However, since this thread is not in the QM interpretation forum, I don't want to get into detail here about how Ballentine deals with QM interpretation/foundations issues vs. other sources--if there is enough interest for that type of discussion I can spin off a separate thread in the interpretations/foundations subforum.
Yes, that's true, one must read it in the context of his earlier review to associate his book with an attack on "Copenhagen". Nonetheless, Ballentine's book rejects the state reduction postulate "This postulate of reduction of the state vector creates a new problem that is peculiar to interpretation A: namely, how to account for the mechanism of this reduction process." (in the text just after Eq 9.9). In other words, his preferred interpretation "B" lacks a fundamental postulate of QM, and the experiment of Section 9.5 is meant to show that interpretations with state reduction as a fundamental postulate are wrong. This is an error, since there are interpretations with state reduction as a fundamental postulate that are consistent with all current experimental evidence, including the experiment in 9.5, and this includes the Copenhagen-style orthodox interpretation.

In case you think that is not a clear enough statement of the state reduction postulate, Ballentine states his rejection of the postulate again in section 12.2 and on p 584.

Also, within the orthodox interpretation, a pure state can be associated with an individual quantum system. However the orthodox interpretation, also contains the Born rule, which means that quantum mechanics only makes probabilistic predictions, and the notion of probability has most usually meant consideration of an ensemble. So in fact there is no difference between correct versions of what he calls Interpretations A and B.

I think this is too strong (as is the claim that Ballentine is "plain wrong on fundamentals"). To the extent Ballentine differs from other sources with regard to which interpretation of QM he prefers, and points out issues he sees with other interpretations, that is not "personal theory" unless every QM textbook that discusses interpretation at all is "personal theory". The fact is that there are multiple interpretations of QM, and with our current state of knowledge, none of them are "wrong" (or "right", for that matter). I think a better description of this aspect (and, as noted above, if more detailed discussion is desired I can spin off a separate thread in the appropriate subforum for that) would be that Ballentine's preferred interpretation is not shared by most other sources, and that one should not use his textbook as one's only source of information about interpretations.
Well, if a fundamental postulate - one that is in many standard texts - is omitted - then how can that not be a fundamental error? Furthermore, Ballentine omits it without introducing any new element, whereas Many Worlds and Bohmian Mechanics omit it but respectively introduce new elements of many worlds and hidden variables (one doesn't have to agree that they are without problems, but they at least agree that you can't drop a postulate without introducing another).
 
  • #15
PeterDonis
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Ballentine's book rejects the state reduction postulate
For "interpretation A", i.e., for interpretations that say the quantum state represents the real, actual state of individual quantum systems. But that is an interpretation-dependent claim. He does not reject "state reduction" when the basic math of QM (e.g., the 7 Basic Rules as we present them here at PF, in the Insights article that the SAs and Mentors created a while back) says to use it; for example, he does not reject using the projection postulate after what he calls a "filter measurement" (i.e., when Rule 7 in our Insights article says to use it).

his preferred interpretation "B" lacks a fundamental postulate of QM
I disagree. See above. It's true that he doesn't emphasize this aspect of interpretation B, but he clearly accepts it, as shown by his discussion of filter measurements elsewhere in the book.

within the orthodox interpretation, a pure state can be associated with an individual quantum system
Which is an interpretation-dependent claim. So you can't say Ballentine is "wrong" for not agreeing with it. All you can say is that your preferred interpretation is different from his.

the orthodox interpretation, also contains the Born rule, which means that quantum mechanics only makes probabilistic predictions, and the notion of probability has most usually meant consideration of an ensemble
This seems to contradict what you just said in the quote from you that I gave before this one. But arguing about what the "orthodox interpretation" says is out of scope for this thread (as I have already said, we can spin off a separate thread in the interpretations subforum if that kind of discussion is desired). The point for this thread is that I don't think you can use the term "wrong" to describe a difference of opinion about interpretations. I described what I think can be said in post #12.

if a fundamental postulate - one that is in many standard texts - is omitted
It isn't. See above. As I said, this is a difference of opinion about interpretation. I don't think it justifies the term "wrong".
 
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  • #16
strangerep
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Hm, yes, I agree that [Ballentine's] argument at the end of the "watched pot" subsection of 12.2 is just handwaving: no math and no explanation, just a bare assertion.
Ballentine (end of sect 12.2 "watched pot") said:
The fallacy clearly results from the assertion that if an observation indicates no decay, then the state vector must be ##|\Psi_u\rangle##. [...]
... which depends on the notion of reduction of the state vector which he criticized and rejected in sect 9.3. So,.... certainly not a "bare assertion". More like "Line so-and-so in your proof is wrong. This invalidates the proof." No need for anything more.

Nevertheless he also references his 1990 paper "Limitations of the Projection Postulate"
(Found. Phys., vol 20, No. 11, 1990, p1329), which does contain more math. Unfortunately, it's behind a paywall.
 
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  • #17
strangerep
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I searched for the book at amazon, which one of these is the first or the second? Amazon.com : ballentine quantum mechanics
The 2nd edition just has extra (important) material on quantum information, but the rest is essentially identical to the 1st edition.

As for the "criticisms" of Ballentine (which I reckon are BS), I have in the past challenged some of his critics to get their arguments published in a reputable peer-reviewed journal (and thus put this nonsense into a form more suitable for discussion on PF). They either ignore me, or abuse me for suggesting that this should even be necessary, which is a mark of crackpottery.

Mindful of Brandolini's Law (a.k.a. the BS asymmetry principle), I refuse to waste any more of my time on this, except to say that you will learn a lot by studying Ballentine.
 
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  • #18
PeterDonis
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which depends on the notion of reduction of the state vector which he criticized and rejected in sect 9.3.
That actually wasn't what I was referring to as a "bare assertion". I was referring to this statement:

Ballentine said:
Here we see that it is disproven by the simple empirical fact that continuous observation does not prevent motion.
There is no argument at all about why continuous observation should prevent motion if the notion he is rejecting were true. Presumably there is more argument in the 1990 paper he references, which, as you note, is unfortunately behind a paywall.
 
  • #19
atyy
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For "interpretation A", i.e., for interpretations that say the quantum state represents the real, actual state of individual quantum systems. But that is an interpretation-dependent claim. He does not reject "state reduction" when the basic math of QM (e.g., the 7 Basic Rules as we present them here at PF, in the Insights article that the SAs and Mentors created a while back) says to use it; for example, he does not reject using the projection postulate after what he calls a "filter measurement" (i.e., when Rule 7 in our Insights article says to use it).
I disagree. See above. It's true that he doesn't emphasize this aspect of interpretation B, but he clearly accepts it, as shown by his discussion of filter measurements elsewhere in the book.
The more straightforward reading of his text is that he rejects the state reduction postulate in the basic math of QM (ie. that Ballentine's QM is not consistent with the 7 Basic Rules) and yet uses it without knowing that he is using it in the filter measurements, and that his text his therefore internally contradictory. At the very least, it is a matter of interpretation of Ballentine's text whether he rejects "state reduction" in the basic math of QM.

Ballentine states his postulates in Chapters 2 and 3 the book. Can the state reduction in the basic math of QM be derived from them? If they cannot, then overall it is not an accidental omission or slight under-emphasis, but a deliberate omission of part of the basic math of QM.
 
  • #20
PeterDonis
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Ballentine states his postulates in Chapters 2 and 3 the book. Can the state reduction in the basic math of QM be derived from them?
See the note in brackets in the Insights article (right after listing various other textbooks).
 
  • #21
atyy
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See the note in brackets in the Insights article (right after listing various other textbooks).
I did not notice that in the Insight before, perhaps it wasn't in the draft I read or I missed it.

Is Ballentine's derivation of state reduction as an effective rule correct? If in the basic math of QM, postulate 7 on state reduction is needed as a separate postulate, then it cannot be derived from the first 6 postulates. Perhaps it can be derived, but as far as I know, there is no consensus derivation of postulate 7 from the first 6 postulates alone. If Ballentine omits postulate 7, then he has to either (1) claim that postulate 7 can be derived from the first 6 postulates (which is not a mainstream claim, although no one has shown it cannot be done) or (2) add postulates that enable the derivation of postulate 7 as an effective rule (which Bohmian mechanics does by adding hidden variables and hidden variable dynamics).

The statement "[Even Ballentine 1998, who rejects rule (7) = his process (9.9) as fundamental, derives it in the form (9.21) as an effective rule.]" in the Insight is also not quite correct. Eq 9.21 is not a derivation of state reduction - that is in the spin recombination experiment in which there is no state reduction in both interpretations A and B. Ballentine introduces state reduction in Eq 9.28, and the question is whether he can justify Eq 9.28 from his postulates, or whether he has simply introduced that as a new postulate.
 
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  • #22
vanhees71
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I think this belongs to the interpretation section of the forum. Whether or not collapse is needed or not is a purely interpretational issue. I don't think that one needs and I also think it's misleading to state a collapse postulate, leading to tons of unnecessary discussions about causality in the relativistic context.

In experiments no collapse occurs, one just measures the values of observables with more or less accuracy and statistical significance.
 
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  • #23
atyy
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within the orthodox interpretation, a pure state can be associated with an individual quantum system.
Which is an interpretation-dependent claim. So you can't say Ballentine is "wrong" for not agreeing with it. All you can say is that your preferred interpretation is different from his.
Ballentine does not have to use the claim that a pure state can be associated with an individual quantum system. However, his error is that he claims that this leads to a form of state reduction that is not supported by experiment. In other words, his criticism of the interpretation is wrong.
 
  • #24
martinbn
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As it has been aknowledged here in the forums, there is more than one version of the CI. I personaly think that CI should be used for Bohr's view. And I don't think he ever talked about collapse/reduction, but I might be wrong.

As to the book, I cannot find anywhere in the text, where he reffers to Copenhagen. So bringing that up is inapproprate for this discussion.
 
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  • #25
vanhees71
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Ballentine does not have to use the claim that a pure state can be associated with an individual quantum system. However, his error is that he claims that this leads to a form of state reduction that is not supported by experiment. In other words, his criticism of the interpretation is wrong.
What precisely is his version of state reduction (I have the book at hand, so for me it's sufficient to point to the section, where the statement is made). AFAIK in the minimal statistical interpretation there's no need for some "state reduction" or "collapse" assumption.
 

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