September 2, 2012:  Giving up on Journal of Physics A
   
    In January, 2011, I became interested in a 2010 paper in Physical Review Letters (PRL)
by J. Dressel, S. Agarwal, and A. N. Jordan entitled "Contextual Values of
Observables in Quantum Measurements" (Phys. Rev. Lett. 104 240401 (2010),
http://arxiv.org/abs/0911.4474 ), to be called DAJ below, along with the authors
as a group.   The Journal of Physics A will be abbreviated as JPA.

[The August 18 entry referred to them by different "pseudo-initials" because I wanted
to focus on the standards of PRL, specifically how easily erroneous material
 is published in PRL and how reluctant PRL is to correct it, or even to make public
that what has been published is disputed.  That is not so practical for this entry because
so many of the external references name the authors.  Also, though the present entry does
 focus on the standards and practices of JPA,  it can also be taken as a commentary on   
the disputed work of  Dressel, Agarwal, and Jordan (and later, Dressel and Jordan alone)
and on the standards of those authors.]

     I questioned the main nontrivial claim of DAJ and wrote the authors about it.
They sent me an attempted proof, to which I found a counterexample (though at that
time I did not have a counterexample to the claim itself).  I communicated the counterexample
to them in messages of February 13 and 14, 2011.  These messages were courteous and
not confrontational.  

    Because of that, I was completely unprepared for their response.  The response was actually
an absence of response; they never acknowledged the counterexample`, and they ignored future
correspondence.   In particular, they ignored a request for their definition of the nonstandard
term "minimal disturbance limit" in DAJ.  They also ignored a request for a valid proof
of the main claim of DAJ (which suggested that the proof followed from routine
power series manipulations which I had not been able to reproduce).

    Later I found a counterexample to the claim itself (not just to the attempted proof which they had
sent me), and posted it in http://arxiv.org/abs/1105.4188v1 .  I also submitted to Physical Review
Letters (PRL) a "Comment" paper containing the counterexample.

    In June, 2011, Dressel and Jordan (but not Agarwal) posted
"Sufficient conditions for uniqueness of the Weak Value" in  http://arxiv.org/abs/1106.1871v1 ,
which claimed to refute my counterexample just mentioned.
The refutation consisted of  adding strong hypotheses to DAJ which the counterexample did not
satisfy, but they did not make this clear.  Some of these hypotheses were not mentioned in DAJ
at all.  One of them, a so-called "pseudo-inverse prescription" for choosing  DAJ's "contextual values"
was very briefly and vaguely mentioned in DAJ, but DAJ did not make clear that it was supposed
 to be a hypothesis for anything.  

    DJ's "Sufficient conditions" paper focused on the pseudo-inverse prescription, ignoring entirely the
additional strong hypotheses which had been added.  I then found a counterexample to the claim
which did satisfy the pseudo-inverse prescription, as well as the additional strong hypotheses of
Version 1 of "Sufficient conditions".   I appended the new counterexample to the first version of
 http://arxiv.org/abs/1105.4188v1 .

[To follow the narrative below, please keep in mind that Version 2 of "Sufficient conditions",
which is the version published in JPA, is substantially different from Version 1.  
Version 2 claims incorrectly that the new counterexample does not satisfy one of the
additional strong hypotheses of Version 1 which had been added to the original claim of DAJ.]

    Meanwhile, I had heard nothing from Dressel and Jordan (henceforth abbreviated DJ),
and my "Comment" submission to PRL was still in progress.  In August, 2011. I wrote to DJ
asking if they disputed the later counterexample which did satisfy the pseudo-inverse
prescription.  In view of the fact that they had been ignoring all of my correspondence,
 I didn't expect a response, but I thought that it might be useful to point out to PRL that
the absence of a response could be taken as a tacit admission that they did not dispute it.  
I was surprised to receive a message from Jordan indicating that they did dispute the
counterexample and would reply to it in a future paper.  He refused to tell me what
they thought was wrong with the counterexample.  

   Months later they did submit the promised paper to the Journal of Physics A (JPA).  
Dressel and Jordan never sent me a copy, but I obtained a copy via the following unusual route.  
On October 19, I received from the Journal of Physics A  (JPA) a request to referee
Dressel and Jordan's paper!  This request is probably a form letter sent without thought,
but its wording is so unusual in the context that it seems worth quoting:

"You have been suggested as a possible expert who could referee the above
paper, which is being considered for publication in Journal of Physics A:
Mathematical and Theoretical. We hope that you will be able to help us."

They want me to referee a paper that criticizes my paper!  What can they be thinking?

     I  replied that it would not be proper for me to referee the paper because of a possible
appearance of conflict of interest, but I did offer to share my expertise by
furnishing a consultant's report which would offer my opinions but would not make
any recommendation for or against publication.  I insisted that in addition the paper
be refereed in a normal way.  

    I also requested that JPA furnish my consultants's report to Dressel and Jordan with
my name attached. I thought that they should have the right to reply.  I was not going
to give any possible appearance of acting as any sort of  "poison pen" referee.
For reasons that utterly escape me, JPA would not agree to this.  

    I finally did send JPA an 8-page consultant's report.  Since JPA would not commit to
sending it to Dressel and Jordan, I sent it to them myself.

[     The consultant's report is quite technical and will interest few; I include the  link to it only to
put on record the information that JPA had before publishing DJ's
"Sufficient conditions for uniqueness of the Weak Value"  J. Phys. A: Math . Theor.
45 015304 (2012) , http://arxiv.org/abs/1106.1871v2 , called "DJ" below, along with
its authors.  There are a few typos, which I have not corrected. ]

    The important elements of the report are:

(1)  The essence of DJ's objection to the latest counterexample
(the one which does satisfy the pseudo-inverse prescription) is that
it does not satisfy a new interpretation of DJ's hypothesis (iv).
If (iv) is interpreted according to standard logical language,
the counterexample is indeed valid, but DJ has come up with a new interpretation
which I had never even considered.  If one gave DJ to 100 competent people  
and asked them what (iv) meant, I would bet that not one would give
 DJ's new interpretation.   Neither (iv)  as normally interpreted
nor DJ's new interpretation (which makes it a hypothesis which is
mathematically very strong with obscure physical meaning)
is even mentioned in DAJ.

(2)  I believe that even under DJ's new interpretation of (iv),
its attempted proof of its main result (which is the main claim of DAJ)
is probably wrong.  At a minimum, it contains a serious gap.

The report did not include the reasons for (2) because they are technical and I was not sure that
they would actually be read.  However, I did offer to discuss the gap in DJ's proof with
the referee, should he read the proof in detail.  This offer was ignored.

    There are many other questionable aspects of DJ, but my report did not dwell on them
(though it did reference arXiv articles which analyzed them).

[One questionable aspect deserves special mention.  Section 3 of DJ criticizes
an earlier counterexample which does not satisfy the pseudo-inverse prescription (PIP),
intimating that this was negligence on my part.  The reasons that it does not are :

(a)  The DAJ paper does not make clear that the PIP is a hypothesis for anything.

(b)  In my correspondence with DAJ back in February when
they were still writing to me, I had specifically asked about the reason for the PIP,
which seemed to me irrelevant to the rest of the DAJ paper.   DAJ's response
was vague and didn't say anything about it being a hypothesis.

(c)  The incorrect attempted proofs of the main claim of DAJ which the group
sent me in February did not assume the PIP, so I knew to a certainty that
when the DAJ paper was submitted, the PIP was not assumed.  DJ added it
later as a hypothesis only after they realized that their initial proof was wrong.]

 In retrospect, I wonder if this was a mistake.  I thought the report was already too long at 8 pages,
and in the light of (1) and (2), I could not imagine that JPA would publish DJ.  To go on about
other misleading statements in DJ seemed at the time like overkill.

    But JPA did publish DJ,  and almost immediately.  DJ was submitted on October 13, 2011,
the final version was received  on  November 11, and the publication date is 
 December 1, 2011.  I have tried to find out from JPA what the referee(s)
 thought of points (1) and (2), but they have yet to furnish any substantive information.  
Given that I took the time to prepare the 8-page report, I find this rather vexing.  If there was
anything wrong with it, or if it were unconvincing for any reason, I would like to know why.
I think that as a courtesy, they should tell me.

    On December 13, 2011, I submitted to JPA two "Comment" papers on DJ, two because
they deal with completely different issues.  One, "Minimizing Detector Variance"  (MDV) is
very short and simple, dealing with DJ's motivation of their "pseudo-inverse prescription"
because it minimizes a certain upper bound to a "detector variance".  MDV points out
that it is easier and more natural to minimize the detector variance itself
(which only requires minimizing a quadratic function)  than to minimize a
particular  upper bound to the detector variance.  I think that this is a useful,
albeit trivial, observation, perhaps overlooked by Dressel and Jordan.  
  
    MDV should take a referee no more than a few days, to review, and that much time
only if the referee had to make a trip to the library to look up the definition of
"Moore-Penrose pseudo-inverse".   However, its status has not yet been decided
approaching nine months after its submission.  It took JPA five months just to send it
to a referee.  

    I suspect that it might have languished indefinitely if I hadn't inquired about it on
May 13, 2012.  After that inquiry,  JPA's website showed that it had been sent to a
referee on May 16, with the report received the very next day!  I have yet to be informed
of the contents of that report.  It was sent to a second referee on May 29,
with no receipt of report noted as of this writing, September 9.

    If it takes JPA eight months and counting to deal with with such a simple paper,  I
despair of it ever coming to a decision about the other, more substantial "Comment"
paper, which I shall call "Proof Gap" .  This is six pages.  A greatly expanded
version is http://arxiv.org/abs/1202.5604.

    "Proof Gap"  points out a critical  error (or at least a serious gap) in  DJ's
attempted proof of its main result, which DJ calls the "General theorem".  
DJ's "General theorem" is the main claim of DAJ, with very strong additional
hypotheses added.

    DJ's attempted proof of its "General theorem" is densely and not
entirely clearly written, and is therefore difficult to read.  I could do so without
excessive labor only because I had already covered so much of the ground
in my own work.  Any referee who is conscientious enough to actually
read it in detail has both my admiration and sympathy.

    Usually, a journal will send a "Comment" paper (e.g., mine) to
the same referee who approved the commented paper (DJ).
If the referee had actually read the proof of DJ's "General theorem" before
recommending DJ for publication, it surely would not take him eight months
to read my much shorter and simpler objection to DJ's attempted proof.  

     If the referee never attempted to read the proof of the "General theorem"
(on which I would give odds of at least 10 to 1),  it might be hard for
him to understand my objection to it.  Could it be that the referee
has been tearing his hair over the proof for eight months?  But if so,
one has to wonder why my paper is subjected to so much more scrutiny
than DJ originally was.  It really does seem likely that there may be a
double standard here.

     DJ was accepted only a month after submission, despite
the fact that JPA (and, one hopes, DJ's referee) was explicitly warned
that there were objections to the proof of the "General theorem".  Had
they accepted my offer to discuss in detail the objections before approval of DJ
for publication, this whole mess might have been avoided.  One doesn't get
the sense that JPA is terribly anxious to assure the correctness of what
it publishes.

    The situation is even worse than just described.  DJ introduces a
new interpretation of its hypothesis (iv) for the "General theorem",
an interpretation which I maintain cannot possibly be deduced from
a reading of (iv) in the light of standard logical language.  My counterexample
satisfies (iv) as normally interpreted, but not as DJ interprets it.  The issue
of whether (iv) actually means what DJ claims is one which
should be decidable by any competent person in very little time.  

    If DJ is wrong about (iv) as I claim, then JPA should have a professional
obligation to publish some kind of retraction.  Only if a competent referee
ruled that DJ is right, would it be necessary to consider the more complicated
question of the correctness of DJ's proof of the "General theorem".  I
explicitly pointed this out in my May 13, 2012 letter to JPA , but have no
sense that anyone has read the letter with understanding.  I have no reason to
think that  JPA has even asked the referee to rule on the simple question of
whether (iv), interpreted by standard logical language, does mean what
DJ claims it means.

    I have written JPA just twice in the 8+ months since the "Comment"s
were submitted.  Both times the publisher (not an editor) replied very
courteously (which I greatly appreciate after dealing with Physical Review
Letters), but I could detect little understanding in the replies.  
I would not expect that a publisher would necessarily understand all the issues
raised, but I would expect that she would forward the letter to someone
who would.  

    I have given up hope that JPA will come to a decision in a reasonable time.
And, if they should come to a decision, in view of previous experiences with them,
I have no confidence that it would be a justifiable decision.  I will not be
surprised if  months or years from now they will reject both "Comment"s for
pretexts such as "too long for a 'Comment' '' in the case of "Proof Gap", or
"too trivial" in the case of "Detector Variance" (the question of why it would take
the better part of a  year to determine these things being ignored).

    Some may doubt that a respectable journal would treat
authors in such a way, but my experience has been otherwise.  Once I submitted a paper
to a well-known journal which held it for over a year, only to issue a
one-sentence rejection on the order of "You should send your paper elsewhere."  
I had enquired about it every few months, receiving minimally communicative responses.
After the rejection, I wrote the Chief Editor asking for the reason for the rejection,
but the letter went unanswered. I would be surprised if the paper was ever read.  
More probably, it was gathering dust in the office of some editor until I enquired
once too often and the editor decided to get rid of this nuisance once and for all.

    I would not be surprised if something similar is happening at JPA.  If the
referee has not  come to a conclusion about "Proof  Gap" in almost nine months,
it seems unlikely that he ever will, or that if he does, his conclusion can be trusted.
The editorial system of JPA seems to allow referees to delay judgments indefinitely.

    I do not plan to enquire again from JPA.  I have already said what I have to say,
and it seems to have fallen on deaf ears.   I will invest no more time in them.