October 27, 2013:  Nearly final results of two years of trying to correct
Dressel and Jordan papers

    In early 2011, I became interested in a 2010 paper of Dressel, Agarwal, and Jordan,
J. Dressel, S. Agarwal, and A. N. Jordan,
"Contextual values of observables in quantum measurements",
Phys. Rev. Lett. 104, 240401 (2010), arXiv:0911.4474
to be called DAJ below,
and wrote the authors enquiring about what I suspected might be serious errors.
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",
        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. A 85, 022123 (2012), arXiv:1110.0418
These proofs  did not actually prove the main claim of DAJ,
but only a greatly weakened version.  
They had to add very strong hypotheses which were not even mentioned in DAJ.

The J. Phys. A (JPA) experience

    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 without consideration of its content
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.  

The Physical Review A (PRA) Experience

The paper to which my Comment referred is cited above.   The "General theorem"
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 of
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.  ... ".
The matrix "Sn"  to which he refers is a matrix "whose rows all sum to zero"
(a direct quote from the DJ's PRA paper).  It is an elementary fact of linear
algebra that such a matrix cannot be invertible, contrary to the referee's unexplained
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.
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.  ... ".

The mentioned "report" of DJ was initially not  sent to me, nor was I informed of its existence.  
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. A 88, 039902 .
It can be obtained without a subscription from this PRA website link.  
The authors have not posted it in the arXiv along with
the papers containing their erroneous claims.

Request to PRL to ask the authors to withdraw their mistaken claim:

    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
"All coauthors have an obligation to provide prompt retractions or correction of errors
in published works. "
Would PRL take this seriously?  My previous dealings with them had given
 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 of
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?"

PRL flatly refused.  Its short reply is here.  

    The form of the refusal is enlightening:
"This is in response to your letter. As we understand it, you are
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."
Notice how my request that they "urge" the authors to submit an erratum is twisted into
 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 could let the authors know of this interest,
inquire if the main claim of DAJ was in fact not proved, and  if so,
suggest that an erratum would be expected.  
This is basically how PRA induced the authors to submit their Erratum.

Letter to JPA

    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 of
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 substance
or conclusions of a published paper are erroneous should promote
the publication of a correction or retraction.'
A similar standard for authors taken from the same website reads:
`When an error is discovered in a published work, it is the obligation
of all authors to promptly retract the paper or correct the results.'
Before commenting on this on my website, I want to be sure that the Board
member's report accurately reflects the policy, practices, and ethical standards
of the highest levels of the administration of the Journal of Physics A."
The authors' admission of the error in the PRA Erratum should surely count as
"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.

Personal conclusions

    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 will be impossible to get anyone to
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.