Papers


Previously, the entries on this page were arranged with the earliest entries first.  But as the page got longer,
I decided that it would be easier to read if the entries were arranged blog-style, with latest first. 
Since the earlier entries are so few, and I don't remember when they were written, I haven't bothered to date them.

August 25, 2014:  Comment on and analysis of Riley paper claiming probability 12% of a magnetic storm worse
    than the  Carrington storm in the next decade.


    See the August 2, 2014 entry for background.  The present entry posts two files.  
    The first is a 3-page Comment paper on

        P. Riley, "On the probability of occurrence of extreme space weather events,
            Space Weather 10 (2012), S02012, available free at
            http://onlinelibrary.wiley.com/doi/10.1029/2011SW000734/abstract .

The second is a 15-page analysis of the Riley paper, of which the Comment paper is
a summary.  

    I am going to submit the shorter paper as a "Comment" paper to Space Weather.
After the Dressel/Jordan experience, it would be reasonable to wonder if I am
a glutton for punishment!

    I'm submitting it just because it seems that having written it, I should make the
effort.  If Space Weather holds it for six months or a year and then rejects it
unrefereed or on some pretext (as J. Phys. A did to the Comment paper on
the Dressel/Jordan mistakes), so be it.  I won't be surprised, and at least
will have the satisfaction of having done what I can.  If the Riley estimates
are taken seriously by policy makers, the cost could be in the tens of billions
of  dollars.

    The Riley estimates are very tedious to check.  I can easily imagine a
referee putting it off month after month until he realizes that to save face,
he must invent some pretext for rejection.  Maybe that is even the
expected outcome, but there are sometimes surprises. 


August 4, 2014:  Comment on "The quantum pigeonhole principle and the nature of quantum correlations
    by Aharonov, et al.


    This entry posts what could be a Comment paper analyzing
Y. Aharonov, F. Colombe, S. Popescu, I. Sabadini, D. C. Struppa, and J. Tollaksen,
    "The quantum pigeonhole principle and the nature of quantum correlations'',  
    http://arXiv.org/abs/1407.3194v1  .  (Note that the version analyzed is Version 1,
    which may not be the latest version when the reader retrieves the article.
This paper summarizes itself (with the summary set in bolface in the paper) as follows:
"The pigeonhole principle: `If you put three pigeons in two pigeonholes,
at least two of the pigeons end up in the same hole' is an obvious yet
fundamental priniciple of Nature as it captures the very essence of
counting.  Here however, we show that in quantum mechanics, this is not
true!  We find instances when three quantum particles are put in two
boxes, yet no two particles are in the same box.''
This is certainly a surprising claim!  The analysis expresses doubt.

    My first reaction after reading the paper was to wonder if anyone would take it seriously.
But a few days ago I found in my inbox a free sample of some articles in Physics World, the
member magazine of the Intitute of Physics (of which I am not a member).
One of them, entitled "Paradoxical pigeons are the latest quantum conundrum",  soberly reports on
the ``Pigeonhole principle" article above, so apparently the editors of this publication do take
it seriously.

    This entry is just for fun, engendered by the Physics World article.   Although it is a serious
analysis of  "Pigeonhole principle", I don't even plan to put it in the arXiv, much less submit
it as a "Comment" paper in case the authors succeed in getting "Pigeonhole principle" published.
If they do get it published (which they probably will), I imagine that many "Comment" papers
will be submitted (but probably few published)!

Added August 30, 2014:  The original Comment has been replaced by Version2.  The exposition
    has been expanded and a bad repeated typo corrected.  If any reader is puzzled by something
    similar, please let me know.  I welcome comments.  
  

August 2, 2014:  Critical analysis of "On the probability of occurrence of extreme
    space weather events" by P. Riley 


   Solar storms emit charged particles which can damage power grids.  The most famous storm occurred
in 1859 and is known as the ``Carrington event'' after the astronomer who documented it.  At that
time there were no power grids to damage, but there were telegraph lines.  It is said that sparking from
current induced in the lines was sufficiently intense to start fires.  The National Academy of Science (NAS)
has estimated that should such a storm occur today, the damages could run into the trillions of dollars.

The problem is that the storm might fry specialized power transformers which take months to replace.
Meanwhile, no one would have power, so commerce would mainly stop.   A summary with a link
to the NAS report can be found at science.nasa.gov/science-news/science-at-nasa/2009/21jan_severespaceweather/  .

    A 2012 paper in the journal Space Weather by P. Riley entitled "On the probability of occurrence
of extreme space weather events" uses a mathematical model developed by the author to estimate
the probability of occurence in the next decade of a storm as strong as the Carrington event as a
surprisingly high 12%.  This figure has been widely cited in the popular press in contexts suggesting
that it is scientific fact.  

    My attention was recently drawn to the matter by a blog in the Washington Post.   Then I read
Riley's paper, which can be downloaded free at http://onlinelibrary.wiley.com/doi/10.1029/2011SW000734/abstract .
I find it unconvincing.  Here is a link to a preliminary analysis of this paper.
There is more to come, but I'm not going to make it public until I have discussed it with the author
(or until he makes it clear that he will not discuss it).  So far, I have received no reply to my inquiries,
but they were only sent a few days ago.  

Added August 25, 2014.  The link to the preliminary analysis has been replaced by a link to
a 3-page "Comment" paper, which is a summary of a 15-page final analysis.
 

July 25, 2014:  Statistical analysis of a famous paper  widely accepted as  proving
    the existence of the photon

    About a month ago, I posted a question to the Internet discussion group sci.physics.research  (accessible
through Google Groups  and  in other ways.)   Its substance was:

Question:  If a quantum particle (a photon, say) enters one port of a beam splitter,  with detectors
    placed in the two output ports,  do both detectors ever fire at once?

The question is somewhat loaded because the very concept of "particle" as an indivisible entity
suggests that the answer is expected to be negative.  Indeed, a negative answer for a sufficiently
weak beam of light entering the beam splitter is taken as evidence for the existence of  particles
of light  called "photons".

    I asked the question because I had seen references that suggested that the answer was known to
be negative, but had never seen this explicitly stated.  A Professor of  Physics at the University of
California at Davis replied that the experiment had been done many times with negative results.
His primary reference was:

    P. Grangier, G. Roger, and A. Aspect, "Experimental Evidence for a Photon Anticorrrelation Effect
        on a Beam Splitter:  A New Light on Single-Photon Interferences", Europhys. Lett. 1 (1986), 173-179

This paper will be called GRA below.

It turns out that the GRA experiment  is  famous..  For example, it was cited by well-known authors as primary
evidence in the Nature review:

    A. Zeilinger, G. Weihs, T. Jennewein, and M. Aspelmeyer, "Happy centenary, photon", Nature 433 (2005), 230-237.
          [This paper mistakenly attributes the GRA results to Clauser, as the authors acknowledge in a Corrigendum.]

And it was acclaimed as "an experimental tour-de-force" in the professor's second reference:

    J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck,  "Observing the
        quantum behavior of light in an undergraduate laboratory", Am. J. Phys. 72 (2004), 1210-1219.

    Initially, I imagined that these references would definitively settle my question.  But on reading them
in detail, I realized that they do not!  First of all, although they address the same question (basically, mine)
using similar methods, their reported results differ by an order of magnitude.  Thorn, et al., after applauding
GRA's  "experimental tour-de-force", never mentions this.  

    Luckily, GRA reports enough raw data to enable a statistical analysis.  (Thorn, et al., does not.)
My analysis of GRA revealed that assuming that the answer to my question was the expected
negative one, the probability of obtaining the reported results of GRA was effectively zero,
less than 10^(-26).

    Far from demonstrating the existence of the photon as seems to be generally believed,
its data reject this hypothesis at a significance level of essentially 100%.   The results  of  Thorn, et al.,
do suggest the existence of the photon, but unfortunately their paper does not include enough raw data
to be sure of this.  (Their paper appears to have the primary objective of  helping
other small physics departments set up similar experiments, and may not have been intended
as a research paper.)

    I have written up my statistical analysis of the GRA results along with brief comments on Thorn, et al.,
in an essay "What happens when detectors are placed in both arms of a Mach-Zehner interferometer",
which can be accessed here .    I will be grateful for notification of any errors.  Comments are welcome.

    This exercise has been a real eye-opener for me.  I have long realized that given the general unreliability
of the theoretical physics literature, the experimental literature is not likely to be better.  But I have
little direct experience with the experimental literature.  Most of of is too abbreviated and presupposes
too much knowledge of equipment for me to judge.  

    Given that this famous GRA paper looks badly wrong and that no one seems to have noticed in over 25
years, I have to wonder how much of the current experimental literature can be trusted.  

    Finally, to avoid misunderstanding, I want to make clear that I do not seriously question the general
belief in the photon, though no reference that I have seen convincingly demonstrates it.  If I had to bet,
I would bet that the conventional wisdom is correct.  But I wouldn't regard the bet as a sure thing,
and I wouldn't bet more than I could afford to lose.

February 9, 2014:

 (1)  Reservations about "Direct  measurement of the
quantum  wavefunction" by Lundeen, Patel, Stewart, and Bamber

(2)  Standards of  J. Phys. A and hopefully final resolution of
    the Dressel/Jordan affair


(3)  Final assessment of the standards of the three mainstream journals involved
    in the Dressel/Jordan affair, Physical Review Letters, Journal of Physics A,
    and Physical Review A


(4)  Concern about the difficulty of genuine peer review in physical science reported
    by others.

 
___________________________________________________________________________________

(1)  Reservations about "Direct  measurement of the
quantum  wavefunction" by Lundeen, Patel, Stewart, and Bamber

    I have many reservations about the widely discussed paper
J. S. Lundeen, B. Surtherland, A. Patel, C. Stewart, and C. Bamber,
"Direct measurement of the quantum wavefunction", Nature 474, 188-191
This paper claims to directly measure a complex quantum wavefunction using weak
measurements, but I question whether their particular uses of weak measurement
formulas are  legitimate.  This is not a question of delicate technical hypotheses,
but or whether common weak value formulas derived in different contexts can be
justified in their context.  The authors are certainly measuring something, but I
question whether it can be identified with a wavefunction.

    I thought of writing a "Comment" paper with my questions/objections (to post on
this website, not to submit to a journal), but their experiment is complicated,
and I can't be sure that I understand it completely.  It seems to me that the parts
about which I am a little vague probably don't affect my reservations,
but I can't be sure of that.    I feel confident about the mathematics,
but less so about its relation to the experiment.

    I will be happy to explain the reservations  to anyone who has read the paper carefully
(including the online supplementary material where some of the important questionable
assumptions are buried) and is prepared to discuss it in detail.  

    When I have thrown out such feelers in the past, I have sometimes gotten  inquiries
of the nature of  "Tell me what you think is wrong with it and then I will read it and
decide if I agree".  Then if I devote several hours writing up my objections,  I may
never hear from the person again.  Please understand and agree that an inquiry
carries an implicit obligation to have carefully read the paper before inquiring and
to be willing and able to discuss it.

(2)  New information on the standards of Journal of Physics A (JPA)

    A letter from the publisher makes clear that  the extreme reluctance of  JPA
to correct erroneous papers which they have published is not some vagary of the
editorial process, but is a practice approved by the highest levels of the journal's
administration.  The letter will be reproduced below, but first I summarize the
situation described in several preceding blogs.  Abbreviations for the relevant
papers are:

    DJ:  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

    P:  Parrott, S.,"Proof gap in ‘Sufficient conditions for uniqueness of the weak value’
         arXiv:1202.5604v6
            This points out a serious gap in the proof of the main result of DJ, and conjectures the
            truth of a restricted version of that result.  (This Version 6 has since been
            updated to Version 7, which discusses DJcorr referenced below.)
          
   DJcorr:   Dressel J. and Jordan A. N., Corrigendum: Sufficient conditions for uniqueness
        of the weak value,     J. Phys. A: Math. Theor. 46 (2013) 029501.  
            This Corrigendum acknowledges the gap exposed by P and attempts to
            prove a Lemma to fill it.  The Lemma, if correct, would not  prove the
            main result of DJ, but only the conjecture which was the focus of  P.  
            The authors seem to believe that the Lemma does prove the main result
            of DJ, but the point is moot because the proof of the Lemma is incorrect,
            and the authors bave not been able to repair it.  The main error is an incorrect
            multiplication of two matrices.

Following is a  summary of the situation up to October, 2013.
(a)  JPA held the Comment submission P for almost a year before
    rejecting it.  They were unable to obtain a referee's report.  (By comparison,
    DJ was accepted in about a month despite the fact that JPA was well
    aware that its main result was disputed.)  The only "reason" given for the rejection
    was that "this course [rejection]  is the most satisfactory [for JPA]".  

(b)  Meanwhile, JPA furnished a copy of  P to Dressel and Jordan , in
    response to which they published in JPA the Corrigendum DJcorr.
    JPA never sought my opinion of DJcorr; I only found out about
    it by accident.

(c)  After noticing the incorrect matrix multiplication which invalidated
    DJcorr, I submitted to JPA yet another "Comment" pointing it out.
    JPA held this one for about six months before rejecting it on the
   pretext that its "claim" that DJcorr's proof  is incorrect had already
    been posted in the arXiv!  Indeed, the author of the rejection (an unnamed
    member of JPA's Editorial Board) went so far as to say that it was not necessary
   for JPA to even consider this claim [that the proof relied in an essential way on
   an incorrect multiplication of two matrices].   This may sound so unbelievable
   that the reader may want to read the short rejection letter reproduced verbatim
   (including unusual formatting) here.

[NOTE added Feb. 25, 2014:  In the originally posted version of this entry, the link
just above  linked to the wrong document.  It linked to the rejection letter for the
Comment P rather than to the rejection for the later Comment on the error of the
Corrigendum DJcorr.

Also, perhaps I should have mentioned that the substance of the refusal to even
consider the "claim" that the proof of DJcorr rested on the incorrect multiplication
of two matrices  is in the short middle section (delineated with "======")
 comprising the Board  members report.  I included the entire email containing
some distracting boilerplate because I was afraid that if I deleted all but
the short Board member's report, it might seem as if I could have
deleted something important.  ]

(d)   The authors had also published the main result of DJ as part of a long
    paper in Physical Review A (PRA), which was written in a different and
    unusual notation:  
Phys. Rev. A 85, 022123 (2012), arXiv:11100418v2
    It is generally considered bad form to publish the same result twice,  
    but perhaps it could be justified in this case  because of the different notations.
    The proof of the PRA paper contained the same error
    [an incorrect matrix multiplication] as DJcorr.
   
        I submitted a similar "Comment" paper to PRA, which initially rejected it
    because of two negative referees' reports.  Neither of these reports
    addressed the issue of the incorrect matrix multiplication!  One of the referees
    admitted that he did not understand the mathematics of the PRA version of DJ's
    proof.  The other referee  recommended rejection on the basis of an elementary
    mathematical error which he made.  It was clear from his report that
    he didn't understand the  mathematics, either.

        I appealed the rejection.   It took the adjudicator three months to report that
    the proof of DJcorr was in fact invalidated because of an incorrect matrix
    multiplication.

        The adjudicator said that my "Comment" could be published (modulo a few
    cosmetic changes), but that it would be better for the authors to submit an
    Erratum instead.   When I initially submitted the Comment, it was sent to the
    authors, who refused to either confirm or deny the error.  In case  this sounds
    almost  unbelievable, I stand ready to furnish evidence in the form of the author's
    reply which PRA furnished.  (Because of the way it was obtained, I don't feel
    comfortable putting it on the website, but I will furnish it privately upon serious
    inquiry.)  After the authors realized that the "Comment" would be published
    unless they submitted an Erratum, they agreed. The Erratum has been published,

        Phys. Rev. A 88, 039902(E) (2013)  
  
    and can  be accessed without a subscription at the PRA website  here .  
    (The authors have not posted it in the arXiv, nor as of this writing corrected
    the posting arXiv:11100418v2 which contains the error.)

    (e)  To get back to J. Phys. A, I wondered if their astounding refusal to even
        consider the Comment pointing out the error in DJcorr might possibly reflect
        not the standards of the journal itself, but instead laziness in evaluating the
        "claim" that the proof of DJcorr was invalid because of an incorrect matrix
        multiplication.  

            [I have observed that many physicists dislike carefully reading proofs.
            I speculated that it might have been hard to find a referee who would
            would rule on the correctness of a proof, for fear of embarassment
            should he be wrong.  Referees typically prefer pronouncements
            so vague as to be impossible to dispute.]

            I wondered if the fact that the authors had admitted the error in PRA might
        make a difference to JPA.  Surely, I thought, the fact that a rival journal
        had corrected the error where JPA refused to even consider the matter might
        reflect badly on JPA.  

            So, I wrote to the publisher of JPA in October, 2013 to find out if its decision
        not to correct DJcorr's error truly reflected the standards of JPA.  The letter is here .
        The reply  received in December, 2013, makes clear that JPA's refusal to correct
        DJcorr  does reflect the low standards of JPA:

            "Dear Dr Parrott,
           
            The Editorial Board and Publishing Staff have given full consideration
            to your appeal on your Comment article with reference to our ethical
            guidelines and I am writing to tell you that we will not be taking any
            further action.

            As you acknowledge, the authors have made corrections in subsequent
            works.  Your Comment does not make sufficient advance beyond these
            subsequent works to merit publication in the journal.  It is not best practice
            to correct all historical articles that have been superceded by amended and
            corrected works and we therefore must consider this matter closed.

            [signed by the Publisher]

I have a few comments on this.  First of all, the above letter to JPA was not an "appeal" to
reverse the decision to reject my Comment.  It was an appeal "to publish some sort
[emphasis added] of correction to the claims of [DJ's 'General theorem'] and the Corrigendum".  
 What I had in mind was inducing Dressel and Jordan to themselves correct DJcorr.
That is what PRA did.  If DJ refused, then JPA could publish the Comment.

    Because the PRA version of DJ's "General theorem" is written in unusual and complicated
notation entirely different from the JPA version, the two may be almost unrecognizable as
essentially the same by many readers.  Few readers of DJ and DJcorr will know that
their main result has been retracted in PRA.  

    At the very least, JPA could add a link to the PRA Erratum in the electronic version of
DJcorr alerting readers that its proof is invalid.  If they didn't want to publish the Comment
and also DJ refused to correct DJcorr, they could add an editorial note to the effect that
DJcorr was disputed, and more details could be found in the PRA erratum.  

    We are talking about a one-sentence notification that readers should not rely on the results of DJ
or DJcorr.  Why would  the publisher consider this "not best practice"?

    It is clear to me that JPA has no interest in correcting erroneous work that they have
published.  

(3)  Final assessment of the standards of the three mainstream journals involved
    in the Dressel/Jordan affair, Physical Review Letters (PRL), Journal of Physics A (JPA),

    and Physical Review A
(PRA

Standards of Physical Review Letters (PRL):

   
PRL published the original announcement of the main result of DJ (see above for
    reference) with  an abbreviated proof in:
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.

This paper contained so many serious mathematical errors that
I cannot imagine that the referee(s)  could have read it with any
care.  The mathematical errors were fundamental, and not of the
nature of the incorrect matrix multiplication of  DJcorr.  That it
was published does not reflect well on PRL's standards.

    [I don't want to make too much of the incorrect matrix multiplication,
    which probably could have happened to anyone in a singly authored
    paper, though its presence  in the doubly authored DJcorr suggests that
    one of the authors may not have been pulling his weight.  But the serious
    mathematical errors in DAJ are of a different nature.

    DAJ should never have been published in its present
    form.  Any competent referee should have caught at least some if its
    questionable statements, as I did. ]

     In February, 2011, I wrote the authors about the errors and asking about
 the sketch of the proof in DAJ of its only nontrivial mathematical claim.
 They sent me an expanded proof which was fundamentally wrong.  I
 replied with my objection, but they never acknowledged it and ignored essentially
all subsequents inquiries about DAJ.  Finally, I wrote up my objections in a Comment
paper and submitted it to PRL.

    This Comment was not well received by PRL.  It took months  to persuade
the editor to even send it to a referee.  I requested that the referee not be one who
had initially approved DAJ, but they sent it to him anyway.  I know this because
his report stated that he had been persuaded to approve DAJ despite misgivings.
He recommended rejection of the Comment on the sole ground that he thought that
it would not be understandable by readers unfamiliar with DAJ.  

    This was an obvious pretext.  Since PRL strictly limits its Comment papers to one page,
it is an obvious impossibility to summarize a complicated paper so that readers
unfamiliar with it could follow all the technical details.  Were this requirement uniformly
enforced, PRL could publish almost no Comment papers.

    I appealed, and the adjudicator (a Divisional Associate Editor) recommended rejection
on the same grounds.  The DAE had the integrity to admit that he did not fully understand
the mathematics of DAJ, and he did not claim that there was any substantive error in the
rejected Comment.

    Although the above and subsequent analysis is critical of PRL, I do want to record a note
of praise.  Unlike JPA,  PRL and PRA have an established appeal process, and part of
this process is that the DAE serving as adjudicator must sign his name to his report.
This is very important.  It distinguishes his review from anonymous referees' reports.
Because the latter are anonymous, referees may suffer little embarassment if their reports
are obviously wrong.  For example, the referees who refused to recognize the incorrect
matrix multiplication in DJcorr would probably have taken more care if they knew
that their identities would be revealed.

    Years later, after the authors had retracted the result of PRA which had been announced in PRL,
I wrote to PRL asking if they might be interested in exploring with the authors the possibility of
an erratum in PRL.  

    [ The false PRL claim was much stronger than the PRA claim which the
    authors had retracted in their Erratum.  The PRL claim is known to be actually false.  The
    PRA claim is not known to be false, though it is known that the proof given in PRA is
    incorrect. ]
  
 Or, if the authors refused to correct their false PRL claim,
would PRL consider another Comment?  The PRL editor flatly refused to raise the issue of an
Erratum with the authors, and stated that once a Comment on a paper had been rejected, no further
Comment submissions on that paper would be considered.

    My conclusion from all this is the same as the conclusion for Journal of Physics A stated above:
PRL has no discernible interest in correcting erroneous work which it has published.

    The lengthy details of my extensive interaction with PRL can be found in the August 18, 2012 entry.

Standards of Physical Review A (PRA):

   
I have long realized that all the Physical Review journals with which I am familiar, including PRL,
PRA, and Phys. Rev. D, publish many papers which are of poor quality and not infrequently outright wrong.  
To detail the reasons for this impression would require many pages which would doubtless
strain the reader's patience.

     PRA's editorial judgement was poor.  It was not necessarily the editor's fault that incompetent referees
were selected, but it should have been obvious from their reports that they were either incompetent or
lacking in integrity (e.g., they both failed to address the incorrect matrix multiplication which was
the essence of the Comment).    

    Also, PRA's published standards for evaluating Comment submissions were not followed.  The published
standards state that the Comment is first sent to the authors of the commented paper, who return a response
(not a formal Reply for publication) which is sent to the author of the Comment.  The very sensible idea is to see
how much agreement might be reached in informal exchanges.  

    However, this was (deliberately) not done in this case.  The editor did send the Comment to the authors,
who returned a response that they had decided to ignore the Comment, even if it should be correct.  This
response was not sent to me until I specifically asked about it.  

    PRA seemed to treat the authors' refusal to discuss their paper or the Comment submission
as completely normal and proper.  In so doing they were actively enabling the authors' "stonewall" tactics.  
It is incomprehensible to me why PRA apparently made no attempt to induce the authors to cooperate
in the evaluation of the Comment prior to the report of the adjudicator of the appeal of the initial rejection.
When the issue is whether two 2 x 2 matrices have been multiplied correctly,
why should it have been necessary to consult two referees and allow a three-month appeal to drag on?  

    That said, of the three journals PRL, JPA, and PRA, without doubt PRA comes out the best.
Despite the many questionable aspects of  PRA's editorial procedures, it does have a defined appeal
process which did work in this case.    The most important erroneous claim of the PRA version of
DJ  was corrected in print.
 
    The details of my interaction with PRA can be found in the October 27, 2013 entry.
(The full details are accessed via a link at the bottom of the entry.}
A brief summary is given above in item (d) of  (2) above (titled New information on the standards
 of Journal of Physics A (JPA)
).


Final assessment of the standards of Journal of Physics A (JPA):


    As regards DJcorr, this is covered above under the "new information" heading,
so I'll just make a few additional remarks here.

    The impression that I have gained from my interactions with this journal is that it
entirely lacks integrity.  Besides the deficiencies noted above, JPA often ignores
correspondence.  

    A typical example is a November 4, 2012 letter raising various issues
which should concern any journal with integrity (e.g., whether the Lemma
of DJcorr would actually prove the claimed "General theorem" of DJ) as DJcorr
asserts. This letter was initially ignored.  After a second inquiry,
 JPA did reply to my request for the referees' reports for
my rejected Comment that they had held for almost a year.
(They admitted that there were no referees' reports apart from
 a few superficial comments from a member of the Editorial Board.)
 The reply which admitted that there were no external referees' reports
promised to reply later to the rest of the Nov. 4  letter, but JPA never did.

    The letter also responds to an astonishing suggestion from JPA.  I had actually
simultaneously submitted two Comment papers to DJ.  The longer and more important
one discussed above pointed out a gap in DJ's main result which it calls the "General theorem".  
The other Comment pointed out a simple way to accomplish something which DJ treated
in a more complicated and less satisfactory manner.  

    The shorter Comment was  rejected on the grounds that it was too trivial.  
[I do not dispute its mathematical triviality, but it is an important triviality which
Dressel and Jordan somehow overlooked in DJ.  There were no external
referees' reports for this Comment, either. ]
However, the author of the rejection (an unnamed member of JPA's Editorial Board)
made the astonishing suggestion that despite its triviality, JPA would consider the Comment
if it were submitted as a paper coauthored with Dressel and Jordan!   Anyone who suspects
that I may be distorting what JPA offered can find it here verbatim.

    Dressel and Jordan had nothing to do with the Comment; in fact they had refused to
communicate with me for months.  Almost all journals consider it unethical to add authors
to a paper who have contributed nothing to it.   That a paper which I alone had written was
considered too trivial for JPA, but would nevertheless be considered if I agreed to add
other authors who had nothing to do with it well illustrates why I consider that
 JPA lacks integrity.

    More details on my interactions with JPA can be found in  the November 23, 2012 entry.  

(4)  Concern about the difficulty of genuine peer review in physical science reported
    by others.


   
My experiences (not just those described above) have convinced me that genuine peer review
in physics is rare.  Journal-based peer review is even rarer.  Similar observations have been made
by others, as described in the interesting article
"Nano-Imaging Feud Sets Online Sites Sizzling" by Robert F. Service,
Science 24 January 2014:
Vol. 343 no. 6169 pp. 358-358   
DOI:10.1126/science.343.6169.358
NEWS & ANALYSIS
 4 Comments.
It describes the efforts of two researchers in Material Science,  Philip Moriarty and Raphael Levy, to
correct what they think are erroneous claims published by Francesco Stellacci and colleagues starting
in 2004.  (I have no knowledge of the substance of the controversy.)

    It took them three years to get their first comments into print in 2012.  (By comparison, my efforts
to correct Dressel/Agarwal/Jordan started in early 2011 and ended in late 2013.)  The slow pace so
frustrated them that they turned to "social media to accelerate this discussion".  

    Stellacci has accused them of "cyber-bullying", which I think is ludicrous.  The article quotes him as follows:

     "Instead of engaging in such 'unethical and unprofessional' conduct, he [Stellaci] says, the skeptics
    should go through the normal channels of peer review and publish their data in journals
    so the scientific process can work through the issues."

That is what I have tried to do in correcting DAJ.    After hundreds of pages of correspondence and
hundreds of  hours of work, the only positive result has been the Erratum  which PRA induced Dressel
and Jordan to publish.  What Stellacci is quoted as suggesting is simply impractical in physics.  

    I would never attempt it again.  Were I not retired, I could never have afforded the time.  
Journals impose such enormous obstacles to genuine peer review as to make it virtually impossible
in many cases, and impractical in most.  

    My experience in trying to correct Dressel/Jordan has turned out to be an unusually graphic illustration
of this.  Even after the issue simplified to a question of whether two 2 x 2 matrices had been correctly
multiplied, two of three journals flatly refused to correct the errors which they had published, and a third
did so only after six months involving two referees' reports, a rejection, and an appeal.  A more complicated
error would likely be impossible to correct in these journals.    

December 6, 2013:  (1)  Recommendation of new paper on
    the possibility of purely statistical 
interpretations of quantum theory;
    (2)  Correction of erroneous Dressel and Jordan papers in J. Phys. A
    still undecided over two months after the publisher promised to
    look into it.


    The following unusually clearly written paper has just appeared in the arXiv:
J. Emerson, D. Serbin, C. Sutherland, and V. Veitch ,  "The whole is greater
    than  the sum of the parts:  on the possibility of purely statistical interpretations of
    quantum theory" , www.arXiv.org/abs/1312.1345v1 ,  abbreviated ESSV   below.
For background, see the July, 2012 entry commenting on a much-discussed paper
of Pusey, Barrett, and Rudolph (PBR) showing that under their (seemingly reasonable)
assumptions, a theory describing the quantum state as a probability distribution
over a collection of more primitive "real" ("ontic") states cannot reproduce the predictions
of quantum theory.  

    ESSV points out that if the seemingly reasonable assumptions of PBR are relaxed,
then the conclusion of PBR cited above no longer holds.  I haven't checked the details
of this later conclusion because I would be rather surprised if the conclusion did hold
under the relazed assumptions.  To me, the interest of ESSV is its extremely clear and
simple presentation of PBR's proof.

    PBR obtains its conclusion from a simple calculation, which is however slightly tedious
to check in detail.  Checking is sufficient to convince the reader that the conclusion is correct, but
doesn't explain the motivation for the calculation.  ESSV does present the motivation
in such a simple way that one can see essentially without calculation that the claimed results
must hold.  

    My dissertation advisor, the late Paul Halmos, used to say that a result that one really
understands should be explainable in essence during a walk without a blackboard.  The
ESSV presentation approaches that ideal.

    Such a clearly written paper is rare in the physics literature.  However, I'm not sure how
easy it would be to read for someone totally unfamiliar with the PBR ideas.  For someone
in that position, I would recommend first reading Matt Leifer's introduction
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/ .
When I first read PBR, I didn't understand the unfamiliar philosophical background,
which Leifer explains very well.  

    After understanding Leifer's introduction, I recommend reading PBR, and finally ESSV.
Even though ESSV's explanation is simpler, it may not be fully comprehensible to someone
totally unfamiliar with PBR.  

Regarding  J. Phys. A (JPA)'s  promised review of editorial ethics relating to correction
of  the admittedly erroneous Dressel and Jordan paper (along with its admittedly
erroneous Corrigendum) which JPA published (See Oct. 27 and Nov. 13, 2013
entries for background):

    No news over two months after the publisher promised to look into it.  
 By comparison, the complicated erroneous paper was accepted  in only a month,
an unusually short tiime, despite the fact that JPA knew that its main result
(its claimed "General theorem") was disputed.  (An offer to discuss specific
objections to its claimed proof with the referee was ignored.)

    When JPA finally settles the matter one way or the other, or when enough time has
passed that it is clear that they have decided to ignore it, I intend to post a final report
on what I have learned about the standards of JPA.  

   
November 18, 2013:  Error in October 23 essay corrected;
   
    update on attempts to correct erroneous Dressel and Jordan papers
       in J. Phys. A.


    I discovered an error in the essay "Restoring the quantum state after a measurement"
posted on October 23, 2013.  It is corrected in a revision, and the link to the original
has been replaced by a link to the revision.

    The October 27, 2013 entry reported the nearly final results of repeated efforts
to get corrections of erroneous Dressel and Jordan (DJ) papers into the literature.  
They were only  "nearly" final because of one loose end.

    In the letter rejecting my "Comment" paper, a  member of the Editorial Board of
J. Phys. A (JPA) had admitted that the proof of DJ's claimed "General theorem"
which they had published was wrong, but nevertheless refused to correct it.
I wrote to the publisher pointing out that refusal to correct known errors
directly violated editorial ethics spelled out on their website.  

    She replied that  she would look into the matter and get back to me.  That was on
October 4, 2013.  I didn't particularly expect to hear from her again, but on November 8
I received a message that she had contacted DJ (after a month!), and would decide the
best way to proceed after they responded.  

     Thus there seems some possibility of a retraction of DJ's claimed "General theorem",
but in view of past experience, I'm not counting on it.

 
October 27, 2013:  Nearly final results of two years of trying to correct
                                      erroneous 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 entry tells the lengthy story of what happened
to that "Comment".

    Subsequently, the plot has thickened.  The original errors were sufficiently
technical that counterexamples were the only practical way to expose them.
The authors added very strong hypotheses which were not even mentioned
in DAJ to invalidate the counterexamples, and they published nearly identical
(except for notation) attempted proofs  in J. Phys. A and Phys. Rev. A):
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 turned out to be wrong, too.  Very recently, after a
"Comment" submission exposing the error,  Phys. Rev. A induced the authors to submit
an Erratum,   
Phys. Rev. A 88, 039902 .
The J. Phys. A (JPA) attempted proof remains uncorrected, as does the original erroneous
claim of the PRL Letter DAJ cited above.  The JPA article may appear to be corrected because
the authors published a Corrigendum to it, but the Corrigendum itself is incorrect because of the
same error that the authors admitted in the Phys. Rev. A Erratum.  

    This error is an incorrect matrix multiplication. Unlike the original errors in DAJ, it is simple
and unequivocal, and one might think that its correction would be routine.  But that isn't how
it worked out.  

    Not only did the authors resist correcting the error, journals themselves
played a major role in enabling this resistance.  It took about six months for anyone
(authors, referees, journals) to even admit that there was an error.  Who would believe
that it could take six months to multiply two 2 x 2 matrices?

    That is the barest outline of the full story.  I think its main interest is not so much the errors
themselves, but how the various journals handle correction of known errors.  The full story
can be found here.
 
October 23, 2013:  Essay " Restoring the quantum state after a measurement"

    The problem of quantum state restoration is the following.

Restoration Problem:  A quantum measurement using "measurement operators" changes the premeasurement state into a postmeasurement state.
For an unknown premeasurement state, is it ever possible  to recover it from the postmeasurement state?  


    A short answer is that it is sometimes possible, but it is usually not possible to do it with certainty.  One has to be satisfied with restoration with a certain probability.  This raises further questions of how to do it with the maximum possible probability.  

    The only general solution I have seen is in the paper:
Cheong, Y. W., and Lee, S-W., "Balance between information gain and reversibility  in weak measurements, Phys. Rev. Lett. 109, 150402 (2012), http://arXiv.org/abs/1203.4909
I hoped to improve on this solution by obtaining a method which would restore the state with a greater probability than that of Cheong and Lee, but detailed calculation revealed that the probability of success with my more general method was exactly the same as that of Cheong and Lee.  Whether this is simply an accident or could be predicted with sufficient insight is unknown (to me, of course!).  I can't help wondering if some as yet undiscovered general principle might be responsible.

    Anyway, in the process of thinking about this problem, I learned quite a lot.  In retrospect, much of it seems somewhat trivial, and I imagine that most of it must be known to someone, but I haven't seen much of it presented in accessible ways in the literature.  I wrote down much  of what I learned in an essay entitled "Restoring the quantum state after a measurement" .  

    Several years ago, there was a flurry of interest in
N. Katz, et al., "Reversal of the Weak Measurement of a Quantum State in a Superconducting Phase Qubit", Phys. Rev. Lett. 101, 200401 (2008)
This reports an experimental implementation of  the restoration problem above.  It was featured in a "Viewpoint" article in the American Physical Society's expository journal Physics , available online without a subscription at  http://physics.aps.org/articles/v1/34 .  The essay comments on the Katz article and the Viewpoint presentation, as well as the Cheong/Lee paper above.  


August 18, 2013:  Six months to multiply two 2 x 2 matrices!

    When I posted the Nov. 23, 2012 blog  about 9 months ago, I expected it to be the last comment on a bizarre situation unique in my professional experience.  But in February, 2013, the situation resurrected itself and has taken an even more bizarre turn, involving two journals, Journal of Physics A and Physical Review A.  

    I expect to report the situation and results after it is resolved, but I can't predict when that might be.  All that I dare say now is that the main result of a certain paper is in error because the authors have incorrectly multiplied two matrices.  They have explicitly  refused to either confirm or deny the error, saying that if there is indeed an error, they will correct it at some unspecified future time.  A brief description of the situation, accurate as of Feb., 2013, can be found in a posting to the Internet "newsgroup" sci.physics.research.  

    Two "Comment" papers pointing out the error have languished for 3-6 months.  An offer to withdraw the first "Comment" (and also withhold the second from submission)  if the authors would retract the claimed theorem was ignored.
[The offer was to the journal, not the authors because the authors refuse to communicate with me.  The journal has ignored a message asking if the offer was passed on the the authors.]  
    Can you believe that a journal could  take six months (and counting!) to resolve the issue of whether two 2 x 2 matrices have been correctly multiplied?  Even after all the unprofessional behavior reported in previous blogs, I wouldn't have, but that is what has happened.

    Now and then I idly speculate on writing a novel based on professional experiences and including this situation.  Of course, I never will, but if I did and described the situation accurately, it would be derided as impossibly unrealistic.  I can scarcely believe it myself.

November 25, 2012:   Possible errors in "A derivation of quantum theory from  physical requirements" by Lluis Masanes and Marcus P. Mueller
   
    The July 1 entry below discussed several recent attempts to "derive" finite dimensional quantum
mechanics from physical principles.  One of the simplest and most clearly written was the paper
of Masanes and Mueller mentioned in the title for this entry,  arXiv:1004.1483v4 ,
New J. Phys. 131: 063001 (2011).  

    My attention was very recently directed to this work, and I began to read it seriously.  It is unusually
clearly written, and much easier to penetrate than some of the other attempts mentioned in the July 1
entry.  I was saddened to find what looks like an essential error in Theorem 2, a key result on which
the rest of the paper is based.  The technical details can be found in the linked  "Comment"  paper.
[Note:  It has been unlinked and replaced with a corrected "Comment" ;  cf. December 6 Update
below.]

    Almost two weeks ago, I sent a preliminary version of the "Comment" to the authors.  There was
a brief acknowledgement from Dr. Masanes, but no substantive reaction to its analysis.  

    A few days ago, I sent a later draft (which differs only cosmetically from the linked version above) to
Dr. Masanes with an offer to withhold it from circulation if he thought there might be anything wrong with it,
until any differences of opinion could be resolved.  There was no response.  Emails to Dr. Mueller
have bounced, and I have been unable to contact him.  

    Normally, I would wait longer before making the "Comment" public because I am acutely aware of the
possibility that I might  have misinterpreted the proof of Theorem 2, and I have no wish to muddy the waters.
However, it looks as if personal circumstances may prevent me from  dealing with this matter for an indefinite
period, so I thought I had better post it now.  If it turns out that it is in error, I apologize in advance both to the
readers and authors.  


[Update December 6, 2012:   After the  above was  posted, Dr. Masanes convinced me that the
conclusion of Theorem 2 is correct, though I still think that the published proof is not clear.  Rather than
withdraw the "Comment" paper,  I have replaced it with a CorrectedComment  , which is identical to the
original except that a proof of Theorem 2 has been added.  This new proof follows explanations of
Dr. Masanes.  I fleshed in the details, and am responsible for any errors. ]


November 23, 2012:  End of Journal of Physics A  experience (?)

    The September 2,  2012 entry described  how two "Comment" papers submitted
 over eight months previously to the Journal of Physics A (JPA) were still in limbo,
 and  how I had  given up hope that they would ever be properly considered.  
These ''Comments" commented on J. Dressel, J., and A. N. Jordan, "Sufficient conditions
for uniqueness of the Weak Value", J. Phys. A:  Math. Theor. 45 015304 (2012).  
This paper will be called DJ below.
On November 2, I received a  rejection letter  for both "Comment"s.  

    The rejection letter included only a report from an unnamed member of the JPA's
Editorial Board,
not a normal referee's report.   Internal evidence suggested that
he probably hadn't
read the longer "Comment" (which I shall call "Proof Gap") with any care.  
The report didn't dispute anything in "Proof  Gap", and didn't give any substantive
reason for the rejection.  The only "reason" given was that rejection was the
"most satisfactory" course for JPA.  

    On November 4, I sent JPA a lengthy letter pointing out several important issues
which the Board member's report had ignored.  The letter also requested the referees'
reports.  

    A week passed without a reply from JPA.  On November 11, I sent them a brief note
stating that I could not guess whether they intended to ignore the issues raised by the letter,
but whatever the case, I would appreciate just the receipt of the referees' reports.  If there
were anything wrong with the "Comment", I wanted to know.  I thought that after waiting
almost a year for their decision, at least they should give me a reason more substantial than
that rejection was the "most satisfactory" course for them.

    After almost two weeks had passed without a reply to that, I assumed that they would
never reply.   I was filled with regret for wasting so much time and effort on "Proof Gap",
in the naive belief that it would be seriously considered.  

    I was surprised, almost shocked, to find today (November 23) in my inbox a message
from JPA.  It admitted that there had been no referees' reports.  They had sent "Proof Gap"
to a referee or referees who promised to deliver a report, but never did.  
They said that they would discuss the issues raised by my November 4 letter and get back to me.

    I don't have any expectation that they will change their rejection decision, and I don't
particularly care  because I am thoroughly disgusted by the whole matter.
However, I do appreciate the integrity of their admission that there were no referees' reports.
I had expected that to avoid admitting that, they would ignore all future inquiries.  Perhaps
my expectations had been colored by Dressel and Jordan's systematic ignoring of  requests
to clarify their published claims, and by the apparent acceptance of this "stonewall" tactic by
both Physical Review Letters and  JPA.

    The Board member's report gave the impression that Dressel and Jordan had promised
to submit an erratum to DJ, an erratum which "will have to acknowledge that this correction
was prompted by Dr Parrott's criticism by quoting the arXiv version [of "Proof Gap"] " .
That would go a long way toward preventing readers of DJ from being misled.  It shows
that JPA has at least some recognition of its professional obligation to correct errors
in what it publishes.

    However, I won't be holding my breath for the appearance of the erratum.  That is the
sort of thing that could be easily deferred until "forgotten".  For all their good intentions,
I doubt that JPA will keep on the heels of Dressel and Jordan.  I'll believe it when I see it.  
   
September 2, 2012:  Standards of Journal of Physics A;
    comments on recent papers of Dressel, Agarwal, and Jordan on "contextual values"


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  .  I found a counterexample to its main nontrivial claim and,
after the authors had begun systematically ignoring inquiries about this paper,  posted it in
http://arxiv.org/abs/1105.4188.  

    About five months later Dressel and Jordan (DJ) published an attempted refutation of
the counterexamples (by this time there were two because DJ added hypotheses to their
original claim in order to invalidate the first counterexample) in Journal of Physics A (JPA).  
This paper was accepted about a month after submission, an unusually short time.

    I submitted two "Comment" papers to  JPA, one very short and simple, and one longer at 6 pages.  
Approaching nine months after their submission in December, 2011, JPA has still not decided what
to do with them.  For the full story, which comments on the standards and practices of JPA and,
implicitly, on the "contextual value" papers  of Dressel, Agarwal, and Jordan,  click on GivingUpOnJPA .


August 18, 2012:  Standards of Physical Review Letters

   
Over a year ago, I had a lengthy experience giving insight into the standards of  Physical Review Letters (PRL),
which is the self-proclaimed "world's foremost physics letters journal" (a quote from its website).
I have been meaning to make it into a journal entry but have put it off because the matter is so distasteful,
and also is not yet fully settled (though it is settled so far as PRL is concerned).  

    In very brief summary, in 2010 PRL published a paper on quantum "weak measurement" which interested me enough to
carefully study.  I questioned the main nontrivial claim of the paper and wrote the authors about it.  They sent me
an attempted proof of the claim, but it was incorrect.  I found a counterexample to the proof (but not to the claim itself)
and sent it to the authors.  (The presentation of the counterexample was courteous, not confrontational.)   They never
acknowledged it, and also ignored several subsequent inquiries about various aspects of their paper.  

    After they did not respond to suggestions that they should correct their paper in an Erratum to prevent future readers
from being misled as I had, I submitted a Comment paper to PRL in late February, 2011.  That began a kind of odyssey
which ended in the rejection of three versions before the final rejection of the fourth version in August, 2011.  Some of these
versions presented  a counterexample to the claim itself (not just to the attempted proof which the authors had sent me),
a counterexample which neither PRL nor its referees disputed.  

    The bottom line is that it seems almost impossible to inject any genuine peer review into PRL. Based on this experience,
I have to conclude that  PRL has almost no interest in correcting erroneous work which it has published.  The lengthy and
convoluted details of my interactions with PRL can be found here .


July 2, 2012:  A recent attempt to rule out "hidden variable" models of quantum mechanics

    ArXiv 1111.3328, to be published in Nature Phys. 3, 476 (2012), by M. Pusey, J. Barrett, and T. Rudolph (called PBR below) has attracted a lot of attention recently.  Version 1 in the arXiv was entitled "The quantum state cannot be interpreted statistically", and though it has been superseded by Version 2 titled "On the reality of the quantum state", I first encountered Version 1 and so will start there. 

    When I first came across Version 1, I didn't understand it, nor why it was arousing so much interest.  I don't mean that I didn't understand its mathematics (which is simple and straightforward), but I didn't grasp its philosophical significance. 

    Then I came across a blog of Matthew Leifer, http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/, which  sets forth its philosophical significance in an exceptionally clear way.  This should really be considered an expository paper, and it deserves to be published, or at least posted in the arXiv. 

    Leifer's explanatory blog has been cited in various published papers, and I think it was probably one of those that drew my attention to it.  I recommend it to any reader before reading PBR.

    The second arXiv version of PBR (which the authors indicate will differ from the published version) adds explanation similar to Leifer's, but not as complete.  Even with this additional explanation, I think that most readers will find PBR more comprehensible if they read Leifer's blog first.

    I hope it was only an oversight that the second version of PBR in May, 2012, did not reference Leifer's much cited November 20, 2011, blog.

    Regarding the substance of PBR, it basically rules out "hidden variable" models for quantum mechanics in a very general context.  I have seen it interpreted as a more general version of Bell's theorem, which also rules out hidden variables, but I don't think this would be quite accurate.  So far as I can see, PBR does not imply Bell's theorem.  The two results start from different hypotheses.  Bell's theorem essentially assumes "locality", that "information" cannot be transmitted faster than the speed of light, while PBR does not, so far as I can see.  On the other hand, PBR seems to assume more of the structure of quantum mechanics than does Bell's theorem.

    This was pointed out by  C. Blood, "A problem with the Pusey, Barrett, Rudolph analysis of the reality of the quantum state", http://arXiv.org//abs/1206.6491, in different language.  He questions whether a particular projective measurement  which the PBR argument requires is physically implementable.  He does not claim that it is not implementable, only that it has not been proved that it is. 

    Since the implementability of all projective measurements is part of the usual formulation of quantum mechanics, the PBR argument still shows that (under its hypotheses), the usual formulation cannot be derived from a hidden variable model.  On the other hand, Blood's observation shows that it is conceivable that a slight weakening of the usual formulation might be consistent with a "hidden variable"  (or "epistemic" in  more current terminology) model.

       I have forgotten where I heard the remark to the effect that

            impossibility arguments mainly reveal a lack of imagination of their proponents,

but I have taken it seriously ever since I lost a bet many years ago.  Someone had proposed the following problem:
 Suppose we have 12 balls, of which 11 are identical and  one "odd ball" is heavier or lighter than the rest (but we don't know which).
 Given a balance scale, determine in no more than three weighings which is the "odd" ball.

I bet that it was impossible, and lost.  My basic reasoning, slightly simplified, was that the first weighing would merely reduce the problem to one at least as hard as a 6-ball problem with two weighings left.  Similarly, that problem would be reduced to a 3-ball problem with only one weighing allowed, which is clearly impossible. Essentially, I thought that binary search would be optimal, and binary search fails.  I think that this kind of reasoning would probably survive scrutiny at most physics journals and many mathematics journals.

    The subtle solution to this puzzle still amazes me.  Indeed, it took me about an hour to reconstruct it (the bet was lost about 50 years ago) even though I more or less remembered the trick.  

    Whenever I see a purported proof of impossibility, I am reminded of my embarrassing loss of that bet.  That is not to say that impossibility proofs have no value; they do because they point out where not to look for a solution.  But I would think very hard before betting good money on the actual impossibility of a conclusion of an impossibility proof.  There is always the possibility that some subtle, unstated hypothesis may invalidate the proof  in practical situations.    

    Before leaving the subject, I should make clear that I haven't checked PBR in complete detail, only one special case which they present first and gives the main idea of their proof.  This special case is mathematically very simple, and their very clever argument shows a hidden variable model cannot account for this special case.

    I include this caveat because I generally try to avoid referencing works for which I cannot vouch in all essential aspects.  (I am speaking generally here; I have no reason to doubt any aspect of PBR.)  This is quite different from the custom of the physics literature of referencing all vaguely related work, presumably without implication of endorsement.
   
    I have assumed that my convention serves readers better, but I am in the process of rethinking this.  It is no secret that the physics literature is generally unreliable (by comparison, a perceived order of magnitude less reliable than the mathematics literature).  How should one deal with a paper whose results are relevant, but about which one has private doubts which one might be reluctant to express publicly?  Reference it anyway? Or ignore it (which would be unethical according a strict reading of the guidelines of the American Physical Society)?  If readers have any thoughts about this, I would be interested in hearing them.


July 1, 2012: Recent attempts to axiomatize quantum mechanics; unreliability of the physics literature

    It has been a long time since the last entry.  I have been active, but have little to show for it.  Last year I became interested in recent attempts to derive quantum mechanics from axioms based on information theory which some consider more intuitive than "usual" axiom systems such as those of von Neumann, Mackey, and Segal.  Some of the papers that I attempted to read (in order of arXiv posting or publication, not order of reading) were:

    Hardy, L., "Quantum Theory From Five Reasonable Axioms", arXiv:0101012v4

    Barrett, J., "Information procession in generalized probabilistic theories",
        arXiv:0508211v3

    Masanes, L., and Muller, M., "A derivation of quantum theory from physical requirements", arXiv:1104.1483v4

    Chiribella, G., D'Ariano, G., and Perinotti, P., "Probabilistic theories with purification", Phys. Rev. A. 81, 062348 (2010), arXiv: arXiv:0908.1583,
         (called CDP10 below)

    Chiribella, G., D'Ariano, G., and Perinotti, P., "Informational derivation of quantum theory", Phys. Rev. A 84,012311 (2011), arXiv: arXiv:1011.6451
        (called CDP11 below)

All of these attempt to derive important parts of finite dimensional quantum theory from axioms which have "operational" meaning, i.e., which might in principle be tested in the laboratory, or at least have intuitive meaning.  By comparison, Mackey's axiomatization of quantum mechanics rests on an axiom which can hardly be considered intuitive:  that the partially ordered set of all questions which one can ask is isomorphic to the set of closed subspaces of a complex Hilbert space.

    The probable influence of the 2001 Hardy paper on the others is evident.  It is written in a refreshingly simple style, with the physical situation very explicitly described.  The other papers start with similar physical setups, but not so explicitly described.  I suggest reading the introductory material in Hardy before attempting any of the other papers.  

    However, I wasn't able to follow Hardy's  mathematics in detail, despite considerable effort.  Some of it is vague, and though presented in a deceptively simple style, it is logically quite complex.  Many of the important arguments are relegated to appendices, where they are not presented in sufficient detail for me to follow.

    So far as I know, this paper was never published, and later Hardy posted a completely  different attempt at axiomatiztion of quantum mechanics:
    Hardy, L., "Foliable Operational Structures for General Probabilistic Theories", arXiv0912.4740 .
I have not attempted to read this later paper in detail. However, I would love to discuss the earlier 2001 paper with anyone who has (or is prepared to) read it in detail. 

    The 2010 and 2011 Chiribella, et al., papers (called CDP10 and CDP11 below, and jointly CDP) have attracted a lot of attention.  For example, they were chosen for discussion in the American Physical Society's expository journal "Physics":  Brukner, C., Physics 4, 55 (2011).  This can be obtained online without a subscription at http://physics.aps.org/articles/v4/55 .

    CDP11 is to some extent a continuation of CDP10.  Both papers are long and intricately complicated. I don't mean just that a few key results have complicated proofs, but that the logical structure of the entire work is intricate.  CDP10 is 40 pages with 64 definitions, 34 lemmas, 30 theorems, and 50 corollaries.  CDP11 is 39 pages with 12 definitions, 78 lemmas, 20 theorems, and 51 corollaries. 

    Here are excerpts from a partial review which I posted on the Internet newsgroup sci.physics.research.  I was hoping (and still hope) to connect with someone interested with discussing these papers in detail, but that search was in vain.  Nobody replied.
 
    There was an article about the CDP result in an expository science magazine which I shall not name in order to avoid identifying some people who were quoted in that article, but who expressed strikingly different views privately.  Having failed to find anyone willing to discuss CDP through internet postings, I wrote to the people who were quoted by that science magazine as commenting favorably on the CDP.  One of them intimated that he had been misquoted.  All admitted that their knowledge of CDP was superficial. None had any interest in discussing the papers.

    I had identified what seemed to me to be some questionable points in CDP.  Having failed to find anyone with any interest in analyzing CDP in detail, I finally wrote to Dr. Chiribella.  I was extremely surprised to find in my inbox, the very next day, a four-page manuscript typeset with complicated mathematical notation, which satisfactorily resolved the points I had raised.  It must have taken hours to produce!

    I went back to reading CDP, and found some more questionable points, which would have to be resolved before further reading would be productive.  I again sent my questions to Dr. Chiribella.  There was a short response that he was very busy at the moment but would answer them when he had time.  That was over six months ago.

    I am sure that no discourtesy was intended.  His initial response far exceeded what I expected, or what I would have had a right to expect.  Because of that, I am reluctant to impose with further inquiries.

    In case anyone else is interested in  CDP, I post here my unanswered second letter to Chiribella (Nov. 18, 2011) detailing what look to me like questionable points in CDP.  It is too technical to be meaningful to anyone who is not actively reading CDP in detail, so if you're not in this category, there is no point to download it.   I post it because it would seem a shame to let my work reading CDP vanish without a trace.  Posting it is very little effort, and there is a long shot that it might conceivably help someone.

    Though it would have been a waste of time to have continued reading CDP without resolving these essential issues, I might continue if they were resolved, or even if I were relatively confident that they could be resolved, e.g, if CDP had been published in a seriously refereed journal.   CDP, which is essentially an intricate mathematical work, was published in Phys. Rev. A, which (like all the American Physical Society journals along with many others) is not known for its reliability.  It is very conceivable to me that CDP has never been read with care by a referee nor indeed, by anyone other than its authors.
 
    This is a depressing situation.  To put it into context, I will start a story which I intend to post in detail in a later entry. 

    Over a year ago, I became interested in claims in a new paper in Phys. Rev. Letters concerning quantum "weak measurement".  It was full of what I later recognized as "hype", and partly because of that I initially didn't realize that its claims were only claims, not based on competent research, and essentially unexamined by competent referees.   The paper omitted so much non-standard information essential to understand it and contained such grievous and elementary mathematical errors that it is inconceivable to me that the referee could have read it with any care.  It should never have been published in anything close to its present form.  (I do not say that it should never have been published at all.)  

    I wrote the authors with several questions about it, and they sent me a purported proof of its main claim.  It was incorrect.  I found a counterexample to the proof, though not to the claim.  I sent the counterexample to the authors, but they did not reply, nor did they reply to subsequent correspondence. (It later became clear that they were deliberately ignoring these inquiries.)  They also did not issue any kind of retraction or correction of the claim.

    Later I found a counterexample to the claim itself (not just to the attempted proof that they had sent me). That set off a year-long effort to correct the claim in the literature, an effort which has still not reached final resolution, and so far has involved something like a hundred pages of correspondence.  Had I realized the extent of the effort, I might well have never undertaken it.  However, once substantial work has been invested, there is always the mirage that a little more might finish the matter.

A Comment paper which I submitted to J. Phys. A , which published one of their incorrect proofs, has been in consideration for over half a year, which may mean that it has never been read carefully and may never be read.  By comparison, the same journal accepted the authors' incorrect proof almost immediately (about a month after submission), despite the fact that they were well aware that it had been challenged.  An offer to discuss my objections to the proof with the referee before publication was ignored.

    That is a bare outline of that situation.  I intend to fill in the details (which are lengthy and quite bizarre) in a later entry.  The point of mentioning it now is to emphasize that mere publication of a claimed result in a supposedly reputable physics journal does not imply that the claim has undergone serious peer review.  I am convinced that papers of a certain complexity by authors with appropriate credentials are routinely recommended for publication simply because it would take referees too much time to analyze them in detail.  Even when later found to be wrong, they are rarely corrected or withdrawn.

    The mathematics refuting the claims of that Phys. Rev. Lett. paper is relatively simple and, I believe, virtually unquestionable.  If there is so much difficulty correcting those claims, imagine the difficulty of locating and reporting errors in CDP, a work which is orders of magnitude (maybe 1000 times) more intricate.  Imagine the investment in time necessary to understand CDP, with the real possibility that in the end, important parts of it might turn out to be in error. 

    That is why the situation seems so depressing. Papers like CDP are often published without meaningful review and most likely never read carefully by anyone (other than the authors). One has to make value judgments on limited information about how to invest one's limited time.  Much as I would like to understand CDP, I have reluctantly decided that the expected value of this investment would be too low. 

    There is an old physicists' joke which goes something like the following:
   "The journals of the APS are expanding on library shelves faster than the speed of
    light, but this does not contradict the theory of relativity because no information
    is being conveyed."
This is mildly amusing because, though distorted, there is more than a grain of truth in it.

November 28, 2010

I have mixed feelings about Wikipedia.  I consult it a lot, but always with reservations.  I've found many articles on strictly mathematical subjects helpful and reasonably accurate, but articles on physics seem much more uneven.  I thought the article on quantum weak measurements, http://en.wikipedia.org/wiki/Weak_Measurement ,  was particularly misleading, and in some ways just plain wrong.  That is where I came across the link to the Discover magazine article
http://discovermagazine.com/2010/apr/01-back-from-the-future claiming that
`
``A series of quantum experiments shows that measurements performed
in the future can influence the present.''

(Needless to say, the article presents no real evidence for this startling claim!)   Although this quote is from the "teaser" to the Discover article, it is presented in the Wikipedia article in a way which suggests the endorsement of the Wikipedia author. 

I thought of rewriting the Wikipedia article, but am hesitant to start what might evolve into a time-consuming controversy, or an "edit war".  As a substitute, I am posting on the discussion page of the Wikipedia article a link to the following SampleArticleOnWeakMeasurements.pdf .  That is how I would rewrite the Wikipedia "Weak Measurements" article, were I to do it.

A huge problem with the Wikipedia model is that the reader has no way to judge the competence or possible bias of authors.  In theory perhaps, questionable articles will eventually be rewritten, but there is no guarantee.  For example, the Wikipedia "Weak Measurements" article has been questionable for years.  It appears to have been originally written by an anonymous author who claims to have earned a Master of Science degree.  The above quote claiming that the future can influence the past was posted by an anonymous editor from an IP address registered to the Procter and Gamble company. 

To pass to another topic, I have been reading "Quantum theory cannot be extended" by R. Colbeck and R. Renner,  http://www.arXiv.org/arXiv:1005.5173v2  , which considers the possibility of  obtaining "standard" quantum theory as a special case of  a more general theory.   An example would be to obtain quantum mechanics as a special case of classical mechanics via an assumption of classical "hidden variables", a possibility which is ruled out (under certain assumptions) by Bell's theorem.  The authors rule out more general possibilities.    However, I am not sure that I can agree with all of their assumptions.  I would be interested in discussing this article with anyone who has been reading it.

October 30, 2010

While browsing the web, I came across an article from the April, 2010 Discover Magazine, entitled "Back to the Future",
http://discovermagazine.com/2010/apr/01-back-from-the-future ,  whose "teaser" summary stated:

``A series of quantum experiments shows that measurements performed
in the future can influence the present.''

Quite a claim!  Direct experimental evidence for influence traveling backward in time! Despite my dubious impressions of the scientific accuracy of Discover magazine, I couldn't resist clicking on the link to bring up the article.

The first page was mainly a reasonably accurate exposition of standard quantum-mechanical ideas.  Then the author, Zeeya Merali, turned on her warp drive and
took off into some kind of intellectual hyperspace.  Quotes and opinions were attributed to well-known physicists which  will (or should) cause many raised eyebrows.  Certainly mine went up.

The article contained a link to another article in the American Physical Society (APS) expository journal Physics 2,32 (2009),
http://physics.aps.org/viewpoint-for/10.1103/PhysRevLett.102.173601 , by S. Popescu, a well-known physicist.  I was astonished to find that the general drift of the Popescu article was much the same as that of the Discover article.  For example, it states:

"... does time indeed flow in two directions in quantum mechanics? ...
 As far as I can tell, Aharonov, Albert, and Vaidman hold the view that one should indeed accept this strange flow of time. I fully agree. Not everybody agrees though, and this is one of the most profound controversies in quantum mechanics.''


Wow!  It certainly was news to me that there was  any controversy over whether time flows forward, backward, or both directions at once (whatever that might mean!), much less that the issue was regarded as ``profound''!

The thrust of the article was that weak quantum measurements somehow validate Popescu's view that ``one should indeed accept this strange flow [both forwards and backwards] of time''.  Since I am very familiar with the mathematics of weak quantum measurements, I eagerly dove into the article to find the evidence for this striking conclusion.

It turned out that the article didn't present any real evidence, and I thought it was highly misleading.   If interested in a more technical analysis, click CommentsOnPopescuPaper.pdf .  (This is nine pages, so may take a noticeable time to download with a slow connection.)  This analysis, originally posted on October 30, 2010, was substantially modified on Nov. 5, 2010.   Nothing in the earlier version was incorrect, but the later version  is  more explicit and considers more plausible guesses at the possible meaning of  undefined symbols in the Popescu paper.  Further minor edits  were made on Nov. 22,  and Nov. 28, 2010.


___________________________________________________________________________________________________________________

Originally, this page was intended for reviews of papers which I read carefully..   But that turned out to be such a large and tedious  task that I abandoned it after constructing partial reviews of a few papers.  Perhaps I shall return to the task at some future time.  But right now, I am reading papers far faster than I could hope to review them.

Brief comments on a few I have recently read follow.
 
Tai-Gon Noh, "Counterfactual Quantum Cryptography'' , Phys. Rev. Letters 103,  230501 (2009)
 Presents a scheme for distributing a cryptographic key  whose main feature, it is claimed, is that "a particle carrying secret information is not in fact transmittted through the quantum channel".   I'm not convinced that the setup descibed will work as the author thinks, but this could be only because I don't understand it properly.  

This paper was featured in the 12/21/09 "This Week in Physics" email distribution by the  American Physical Society (APS), with headline  "The mere possibility of  a  quantum transmission, rather than its actual occurrence, may enable key distribution in quantum cryptography".  I would be interested to hear from anybody who has read this paper carefully and either has doubts or believes it sound and would be willing to answer questions about it.

L. Heaney, A. Cabello, M.F. Santos, and V. Vedral  "Extreme non-locality with one photon" ,  arXiv: 0911.0770v1.
Very interesting "all-or-none" theorem in which a certain result must occur with certainty for local theories, but has vanishing quantum-mechanical probability in a certain limit.  Uses bosonic symmetry of photon wave-function, uncommon in Bell-type arguments.  I had some trouble reading this, but eventually decided that it seems basically sound, though parts of it are still obscure to me.

   
Around October,  2009

 
    My recent paper, ``Quantum weak values are not unique.  What do they actually measure?" , was rejected by Foundations of  Physics, largely because of partial overlap with  an interesting recent paper of R. Jozsa, "Complex values in quantum measurement", Phys. Rev. A 76, 022103 (2007).   I question whether the overlap is sufficient to justify rejection, particularly since the Jozsa paper relies on uncontrolled approximations and therefore is less mathematically rigorous.  However, I don't plan to submit it elsewhere.  I don't think the mathematics in the paper (mainly finite dimensional linear algebra) is  sufficiently interesting for  the Journal of  Mathematical Physics,  and I can't think of  another good journal where it might get a careful reading. 

    To see the referees' reports  along with comments on them, click on refcom.pdf .     The version of the paper on which the referees report  is Version 2

    Useful  comments of  one of the referees are incorporated in  Version3.pdf .     This version is mathematically almost  identical to the original, but some of the exposition has (hopefully!) been improved and the Jozsa reference added, along with an an "Afterword" section.    This will be submitted to the arXiv in early Jan., 2010.

       Problems are not expected, but  I have had past problems with arXiv submissions which included referees' reports (even anonymous ones).  They claim there might be some issue with copyright violations, but that seems to me farfetched and hypocritical, given that they archive numerous copyrighted papers with typography which makes it likely that they were directly copied from the APS website ("PROLA").  There seems to be a culture of  "don't ask, don't tell" regarding copyrighted material in the arXiv.  My "Version 3" does not directly quote the referees' reports (paraphrases are OK, or at least were previously), and only refers to them in passing, so I'm not expecting problems.

    It seems  unfortunate that the arXiv  prohibits referees' reports.  In theory, these are supposed to be careful peer review.  Why should journals object to authors making them public?  (I  have never heard of any journal that has objected, which makes the arXiv's sensitivity to the issue even harder to understand.)  In my case, I want potential readers to know why the paper was rejected, and in particular that there was no objection to its mathematics.