erroneous

In early 2011, I became interested in a 2010 paper of Dressel, Agarwal, and Jordan,

J. Dressel, S. Agarwal, and A. N. Jordan,and wrote the authors enquiring about what I suspected might be serious errors.

"Contextual values of observables in quantum measurements",

Phys. Rev. Lett.104, 240401 (2010), arXiv:0911.4474

to be called DAJ below,

The published proof of its only nontrivial result was very sketchy, and they sent me a

more extensive version.

However, it was wrong. I sent them my objection, but they never replied.

Over the next few months, I enquired about various points in DAJ, but received

no replies. When it became clear that they were deliberately ignoring all inquiries,

I submitted a "Comment" paper on DAJ to Phys. Rev. Lett (PRL).

The August 18, 2012 blog below tells the lengthy story of what happened

to that "Comment". In short, it was rejected, but not for any reason connected

with its mathematical correctness.

PRL urged the authors to publish elsewhere a complete proof of the main claim

of DAJ. Authors Dressel and Jordan (DJ) published essentially the same proof twice

(though in different notations), once in J. Phys. A (JPA),

and a few months later in Phys. Rev. A (PRA):

Dressel, J., and Jordan, A. N., "Sufficient conditions for uniquness of the weak value",These proofs did not actually prove the main claim of DAJ,

J. Phys. A: Math. Theor.45 ,015304 (2012), arXiv:1106.1871

Dressel, J. and Jordan, A. N., "Contextual-value approach to

the generalized measurement of observables",

Phys. Rev. A85, 022123 (2012), arXiv:1110.0418

but only a greatly weakened version.

They had to add very strong hypotheses which were not even mentioned in DAJ.

There was a major gap in this proof, and I submitted a "Comment" paper to JPA

exposing it. JPA held this "Comment" for almost a year before rejecting it unrefereed on the

sole ground that rejection was "the most satisfactory" course for JPA. The story of

that JPA experience is told in the Sept. 2, 2012 and Nov. 23 entries.

JPA had been in correspondence with the authors, who admitted that there was

a gap in their published proof. They proposed to submit a Corrigendum which

would prove a lemma to fill the gap.

They did submit the Corrigendum, which JPA published. I do not know if JPA

scrutinized its accuracy in any way, but they never sought my opinion of it.

The Corrigendum's proof of its Lemma was wrong due to an incorrect matrix multiplication.

When I noticed this after publication, I submitted yet another "Comment" to JPA.

They held this one for six months before rejecting it

for the sole stated "reason" that its substance had already been posted in the arXiv,

and anyone interested could read it there!

I realize that this must sound almost unbelievable, and I imagine that many readers

may be skeptical that I am presenting the matter accurately.

They can read the rejection letter here.

The "general theorem" mentioned in the letter is what the JPA paper calls its main result.

It is the main nontrivial claim of DAJ with additional strong hypotheses added.

Note that the letter's anonymous author (a member of the Editorial Board of JPA)

explicitly recognizes that DJ's claimed "General theorem" (GT) is actually unproved

because he invites me to prove it! JPA knows full well that the proof of the GT

which it published is wrong, and it refuses to publish a correction.

Along with the submission to JPA of the "Comment" on the Corrigendum, I offered

to withdraw the "Comment" if the authors would retract the "General theorem" from all

journals in which it had been claimed, including PRL, JPA, and Phys. Rev. A (PRA).

When no reply had been received after a month, I submitted a "Comment" to PRA

similar to the "Comment" on JPA's Corrigendum.

of the JPA paper is simply called "Theorem" in the PRA paper. It is the only result in

either paper dignified with the name "theorem".

The attempted proof of the "Theorem" rests on a lemma which is the same as the JPA

Corrigendum's "Lemma", but it is called "Lemma 1" in the PRA paper. In the context of

the Theorem's proof, Lemma 1 is essentially a special case of the Theorem.

The mathematically identical proofs of the Lemma in the JPA Corrigendum and

of Lemma 1 in the PRA paper are invalidated by an incorrect matrix multiplication.

The matrices incorrectly multiplied can be as small as 2 x 2.

The rejected "Comment" on the JPA Corrigendum and the PRA "Comment" are similar.

Their only mathematical content is to point out the incorrect multiplication.

There is a link to the JPA Comment above, and the PRA Comment is here.

One could hardly imagine a simpler and more unequivocal error.

Yet it was not recognized by either of PRA's two referees.

The first referee dodged the issue of the correctness of the Comment,

basing his objection on several obvious pretexts, such as an objection

that I had not demonstrated the usefulness of DJ's Theorem. His other

objections were similarly specious, and this should have been obvious even

to an editor unfamiliar with the technical content. Moreover, the referee

himself admitted that he did not understand the mathematics of the DJ

paper. That in itself should have been sufficient reason to discount

the report.

I will be happy to furnish a copy of the report to any sincerely interested person.

The same goes for all documents mentioned.

The second referee's report was badly mathematically incorrect.

The first paragraphs read:

"The most important thing is to ensure the validity and correctness ofThe matrix "Sn" to which he refers is a matrix "whose rows all sum to zero"

whatever is being published as a scientific result, this applies to

the comment under consideration as well.

Based on this, I believe that the comment under consideration is not

worthwhile as its main point is not valid. The issue raised has

already been addressed in a reply from Dressdel and Jordan to another

prior comment by the Author on their work on the same theorem. The

counterexample provided in this comment fails to satisfy the

conditions state by Dressdel and Jordan as necessary for their Theorem

to hold. These conditions are clearly explained in [J Dressel and A N

Jordan 2012 J. Phys. A: Math. Theor. 45 015304]. Condition (iii,iv)

therein states that the Sn must be invertible, i.e. it must *not* hold

that det[Sn]=0. The Author has given a counter-example in which

det[Sn]=0. This makes the counterexample is invalid, just as the

others he has given in previous comments. It is on this basis that I

strongly recommend that the manuscript not be accepted for publication

as a Comment in PRA. ... ".

(a direct quote from the DJ's PRA paper). It is an elementary fact of linear

algebra that such a matrix

belief that "Sn must be invertible".

The editor has a Ph.D. in physics, and ought to know enough linear algebra

to recognize the referee's error when it was pointed out, or at least to sense that

something is fishy which should be investigated further. Yet when I did point it out,

and requested that the Comment be sent to a mathematically competent referee

(just about any mathematician would do, and I suggested several), she flatly refused.

To put into context what happened next, I need to backtrack a little. The PRA

website describes its procedure for handling "Comment" papers:

"(1) The paper is first sent to the author(s) whose work is being criticized.The mentioned "report" of DJ was initially not sent to me, nor was I informed of its existence.

These authors act as reviewers (usually not anonymously) and should provide a report

(not a Reply) suitable for transmittal to the author(s) of the Comment.

(2) After suitable exchanges between the involved parties, the Comment,

along with relevant correspondence, is sent to an uninvolved referee for anonymous review. ... ".

After I specifically requested it, they did send it. The content was astounding.

The reply came from Jordan, though I assume Dressel must have approved it.

He specifically refused to address the issue of the correctness of the Comment!

He said that if there were in fact an error, they would either submit an erratum at

some unspecified future time or correct it in some future publication.

Remember, we are not talking about a complicated alleged error

which might be time-consuming to resolve. The issue is

whether two 2 x 2 matrices have been correctly multiplied!

Even more astonishing to me than their blatant "stonewall" tactic is that

PRA apparently accepted it as perfectly normal and proper. Were I an editor of PRA

confronted with such a situation, I would send the authors a blistering letter

reminding them that submission of a manuscript entails a professional responsibility to

cooperate in resolving any issues arising from it.

For most, refereeing is an unwelcome, time-consuming chore.

By refusing to admit their error initially, Dressel and Jordan deliberately

wasted the time of two referees, an employee editor,

and a volunteer Divisional Associate Editor who handled the appeal (see below).

And to all appearances, this was perfectly OK with PRA.

Unlike JPA, PRA has an appeals process, and I appealed. The appeal goes to

a Divisional Associate Editor (DAE) selected by the employee editors.

After three months of consideration, the DAE reported that the authors had, in fact,

incorrectly multiplied the matrices and that this invalidated the proof of Lemma 1.

He said that the Comment could be published (modulo a few minor expository changes),

but that it would be better to ask the authors to submit an erratum instead.

They agreed to do so, and it has been published in

Phys. Rev. AIt can be obtained without a subscription from this PRA website link.88, 039902 .

The authors have not posted it in the arXiv along with

the papers containing their erroneous claims.

Recall that the "Theorem" of DJ's PRA paper was a greatly weakened version of

the main nontrivial claim of their PRL Letter DAJ cited above. Now that the authors had

admitted in the PRA Erratum that they could not prove even this weakened version,

I wanted to see what PRL would do with this information.

The Guidelines for Professional Conduct on the American Physical Society's (APS) website

include:

"All coauthors have an obligation to provide prompt retractions or correction of errorsWould PRL take this seriously? My previous dealings with them had given

in published works. "

the strong impression that they would not, but I did not know this,

and I had to consider the possibility that they might.

I sent a letter to PRL outlining the present situation on Oct. 3, 2013.

You can access the letter here , but I must warn that is long and

repeats much of the above account. The letter asked the following:

"Finally, I come to the point of this letter. I want to avoid submission ofPRL flatly refused. Its short reply is here.

another Comment to PRL. It seems clear that the most graceful way to resolve

the matter would be for PRL to urge the authors of DAJ to submit an erratum.

Is PRL willing to do so? If not or if the authors refuse, is PRL willing to

consider another Comment, given the tectonic change in the situation since the

last one was submitted?"

The form of the refusal is enlightening:

"This is in response to your letter. As we understand it, you areNotice how my request that they "urge" the authors to submit an erratum is twisted into

requesting one of two things:

a) that we "urge the authors of DAJ to submit an Erratum"

b) that we "consider another Comment" [from you]

I am afraid both of these things violate our policies. We do not force

authors to submit Errata and authors are allowed to submit no more

than one Comment on a Letter. Further, the case of your one allowed

Comment is closed."

a request to "force authors to submit Errata", which obviously they cannot do.

But if they were at all interested in the integrity of their publication,

they

inquire if the main claim of DAJ was in fact not proved, and if so,

This is basically how PRA induced the authors to submit their Erratum.

The authors' Erratum which publicly admits the error in PRA's Lemma 1

(the same as the error in their JPA Corrigendum) was published about a month after

the JPA rejection of the "Comment" pointing out the error. I wondered if knowledge of

the Erratum would make a difference to JPA. I wrote to all the administrators of JPA

named in their previous correspondence informing them of this:

"The purpose of this letter is to make sure that you are aware that the report ofThe authors' admission of the error in the PRA Erratum should surely count as

the Board member in the copy below of your 19 August email directly violates

the following standard of editorial ethics taken from your website:

`An editor presented with convincing evidence that the substanceA similar standard for authors taken from the same website reads:

or conclusions of a published paper are erroneous should promote

the publication of a correction or retraction.'

`When an error is discovered in a published work, it is the obligationBefore commenting on this on my website, I want to be sure that the Board

of all authors to promptly retract the paper or correct the results.'

member's report accurately reflects the policy, practices, and ethical standards

of the highest levels of the administration of the Journal of Physics A."

"convincing evidence"! I wondered if JPA would take seriously

the standard of editorial ethics just quoted. The full letter can be found here.

I was rather surprised to find a courteous reply from the publisher the very next day.

It said that she understood why I was "dissatisfied" with the handling of my two "Comment"

submissions, and she would "contact you again soon".

It is now October 27, so that was almost a month ago. I don't particularly expect to hear

from her again, but if I JPA should decide to act in accordance with the fine words quoted

above from their website, I will report that here. Apart from this loose end,

the experience of trying to get into the literature corrections of erroneous claims

seems to be at a welcome end.

Despite the fact that most journals have some nominal procedure to

dispute published claims, in practice it is almost impossible to do so.

If an error is at all complicated, it probably

examine it carefully. That was the case with my original PRL comments.

Even if the error is simple and unequivocal, as with the Corrigendum's incorrect

matrix multiplication, there is likely to be enormous resistance to recognizing it

if the authors refuse to acknowledge it. The JPA and PRA experiences provide

many examples. This has happened so often and in so many ways

that I am convinced that it is typical.

Were it not for the integrity and competence of one Divisional Associate Editor,

my PRA "Comment" might well have been rejected, in which case the erroneous claims of

Dressel and Jordan would almost certainly have gone entirely uncorrected in the literature.

They remain uncorrected in PRL and JPA.

The whole affair has been an interesting experience, but so enormously time-consuming

and frustrating that I would not do it again. If I find errors in published works, I plan to

limit myself to commenting on them on my website.

This situation should not exist, but I don't see what can be done about it.

The important thing may be to recognize it. Inexperienced researchers may not realize

that in physics, meaningful peer review is almost nonexistent.

The two incompetent referees' reports on the PRA "Comment" should give pause to

anyone submitting a paper in the naive expectation that it would be carefully considered

by competent individuals. Remember that the issue here was whether two 2 x 2 matrices

had been correctly multiplied! At a minimum, one would expect that the referees

would recognize the incorrect multiplication, but neither did. And one would expect that

an editor with a Ph.D. in physics would realize that something could be awry

when a point so elementary was disputed.

If an unknown Einstein were to try to publish today, I would not give even odds that

he could succeed. It reminds me of places I have lived where political corruption is

so endemic that one doesn't expect anything else. One simply adjusts to the reality.