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Supposed distribution of dark matter in the Universe. Credit: NASA/UNC



The Adler Report
Aug 03, 2009

Contributing editor Dr. Thomas Wilson recently drew attention to an article in the Journal of Physics A (JPA) that purported to place direct limits on the mass of earth-bound dark matter and that presented a misleading interpretation of confidence intervals.

After reading Dr. Wilson's article, as well as the original JPA paper, Dr. Jeremy Dunning-Davies, Senior Lecturer in Theoretical Physics in the Department of Physics at the University of Hull, England, sent a protest directly to Professor Patrick Dorey, the JPA editor, concerning material of such dubious quality being accepted for publication. The reply and subsequent communications are related below.

Readers are encouraged to review the detailed commentary, but the outcome is easily summarized. Drs. Dunning-Davies and Wilson pointed out basic errors in Adler's article to the referees. They also objected to a lack of correct review at the Journal that resulted in sensational claims propagating into the popular media. As expected, the referees reacted emotionally to the criticism and rejected the comments for publication.

In summary, the entire process can be described as:

* A “fast-track” article was published with misleading interpretations of data in a mainstream physics journal, probably because it mentioned dark matter in Earth’s immediate neighbourhood (i.e. sensational claims).

* Referees missed these basic errors, indicating a failure of the review process.

* No one besides Drs. Dunning-Davies and Wilson responded to the errors, revealing a general blindness in scientific critical thinking.

* Mainstream popular science media published and expanded on the “findings,” demonstrating a lack of critical thinking in the science media.

* When a critical review of the article was submitted, the referees reacted emotionally and rejected an alternative view, showing a lack of professional scientific conduct.


Dear Jeremy Dunning-Davies,

Many thanks for your message concerning the FTC by Adler. I'm sorry for the slow reply, but we wanted to dig out the original referee reports, which took longer than expected. All I can say is that the referees were all respected workers in related fields, and were happy with publication. So I think that procedures were correctly followed. On the other hand, if you do feel that important points were missed which deserve to be brought to wider attention, you would be very welcome to submit a "comment" to the journal at (which would also be refereed, of course).

With best wishes,Patrick Dorey.


Dear Professor Dorey,

Thank you so much for taking all the trouble you obviously have taken over my letter. I assure you it is appreciated. I feel I should state, though, that I never had any real doubt that correct procedures had been followed. I'm rather more concerned that some referees don't actually do the job they're supposed to do and, on occasions, if something appears to conform to conventional wisdom, they will accept it on the nod, so to speak. I will indeed look at the Adler paper again and may take up your suggestion to submit an official comment.

Thank you once again,

Jeremy Dunning-Davies.


Editor's note: As a result of the above email exchange, the following response article was submitted to JPA by Drs. Wilson and Dunning-Davies:

Some comments on ‘Placing direct limits on the mass of earth-bound dark matter’
By Stephen L. Adler, J. Phys. A: Math. Theor. 41 (2008) 412002


Claims made concerning limits on the mass of possible earth-bound dark matter in a recent paper by Stephen L. Adler are examined afresh and doubts are raised.

In this short article by Adler, it is claimed that a method is introduced for calculating the maximum amount of dark matter that must be present in the space between the Laser Geodynamics Satellites and the Moon’s orbit. The method suggested is deceptively simple. The author indicates that this quantity of dark matter is given by subtracting the values of the product of the universal constant of gravitation and the mass for the earth and the moon from the value of the same product for the two combined.

This is summarised in equation (4):

GMdm = GMcombined – GMe – GMm .

Published data is then used to give an estimate of the expected answer.

The first query concerns the alternative method for determining the moon’s mass by studying the orbit of a close passing asteroid which is influenced by both the gravitational field of the moon and that of the earth. It is pointed out that, from such an analysis, one may find an accurate figure for the ratio,

where ΔMe and ΔMm denote possible contributions from earth-bound and moon-bound dark matter.

Hence, to a first approximation

where δ =



Due to this relationship, one must enquire as to why the third term on the left-hand side of equation (5) is as it is. However, if this equation is correct, the claim following equation (7) is certainly of dubious validity since, to arrive at this result, so many approximations have been made. Therefore, the claim of a ‘potential one percent accuracy’ must be open to doubt.

A numerical evaluation then follows and this raises even more serious queries. Firstly, each of the separate values of the product GM is found by different methods, each involving different sets of assumptions. The figures are then manipulated in different ways, again with implicit assumptions, before the final calculation. After all this, the GM for dark matter is found to be 0.0001±0.0016 which, on dividing by the value of GM for the earth leads to a ratio of (0.3±4)×10^-9. Based on this, it is asserted that there must be a mass of dark matter less than 4×10^-9 times the mass of the earth in the volume of space considered – assuming G constant.

There are two problems we can see with the conclusion above. The first problem concerns the statistical significance of 0.0001±0.0016. The second problem concerns the assertion that there must be a mass of dark matter less than 4×10^-9 times the mass of the earth in the volume of space considered. Let’s consider each in turn.

Adler’s value for the combined Earth-Moon GM is 403,503.2357 ± 0.0014. If for comparison we add the separate Earth and Moon values and use standard interval calculations to get the new error, we get 403,503.2356 ± 0.0011. If you look at these two values with error bars on a chart, the second summed value fits perfectly within the 95% confidence error bars of the original combined value. There’s no significant difference between the two values. Yes, you can do some misguided mathematical calculations to derive a difference value of 0.0001 (“in the noise” so to speak), but it’s not meaningful.

Consider now the ratio (0.3±4)×10-9. Adler uses this value to assert there is at most 4×10-9 times the mass of the earth in the volume of space considered. However, it follows that -3.7 is as statistically valid as +4.3. The best that may be deduced is that there is a 95% likelihood of there being, or not being, any dark matter in the stated volume of space. We’re not sure that is really very interesting; certainly not a result justifying a Fast Track Publication.

Whatever one’s belief on the existence, or not, of dark matter, probably the most important comment in the paper occurs in footnote 5, where the author comments that the analysis in the paper is based on purely gravitational considerations. It must always be remembered that other forces could be exerting influences also. Finally, although this paper seems to have been lauded in both the Scientific American and the American Scientist, apparently because it lends credence to the notion that dark matter exists, it has to be acknowledged that other reasonable explanations exist for the other observed effects to which those articles refer in the context of this one by Adler.


The initial response from the journal, together with subsequent correspondence, now follow:

Ref: A/315310/COM/973Dear Dr Dunning-Davies.TITLE: Comment on "Placing direct limits on the mass of earth-bound dark matter"AUTHORS: Dr Jeremy Dunning-Davies et alYour comment submitted to Journal of Physics A: Mathematical andTheoretical has now been refereed and the referee report(s) are attached.I am sorry to tell you that the referee(s) have recommended that yourcomment should not be published in Journal of Physics A: Mathematical andTheoretical, for the reasons given in the reports. Your comment hastherefore been withdrawn from consideration.I would like to thank you for your interest in Journal of Physics A:Mathematical and Theoretical.Yours sincerelyDaniel Heatley and Paul Fishman - Publishing AdministratorJournal of Physics A: Mathematical and TheoreticalArticle under review for Journal of Physics A: Mathematical and TheoreticalComment on "Placing direct limits on the mass of earth-bound dark matter" -Dr Jeremy Dunning-Davies et al


I do not view this article as appropriate for the Journal, and it should not be sent out for normal refereeing. The tone of the article is quite inappropriate, and the article really seems to be attacking Dr Adler's article on the grounds that it received publicity in Scientific American and the American Scientist. The technical criticisms that the current authors bring up against Dr Adler's article are wrong. Dr Adler's key conclusion in his article is the quite proper and perfectly correct statement that that "the mass of earth based dark matter lying between the moon's orbit ... and the LAGEOS orbit ... must be less than 4 x 10^{-9} of the earth's mass, AT A 1-SIGMA CONFIDENCE LEVEL''. (my emphasis) The current authors have set up a "straw man" by systematically ignoring all of Dr Adler's cautionary qualifying statements, and have effectively attacked statements he did not make. This comment is utterly inappropriate for publication.


Dear Miss Gillan,

Thank you for your communication. However, I feel I must raise some queries over the decision not to accept the comments by Dr Wilson and myself. I originally wrote to Professor Dorey about the original article by Adler, pointing out that, in that article, nothing concrete had been proved and it did not reflect well on the journal that it had been accepted for publication with such seeming undue haste. His reply is reproduced below and, as you can see, he states that I'm welcome to submit a comment which would be refereed! Hence, the submitted comment should have been refereed.

Also, it's unclear from the Board member's comments why our criticisms are considered "wrong".  He doesn't explicitly indicate where we are in error when we state that Adler's mathematical conclusion equally implies both the positive presence of dark matter as well as the nonsensical notion of the negative presence of dark matter (a negative value for the dark matter mass). The response seems to be rather emotional and, quite frankly, gives the distinct impression that he knows they've been caught out.

Further, if criticism such as ours is to be stifled, how can true science be expected to progress? In the comment we submitted, there is very obviously no setting up of a 'straw man'; we have commented only on statements contained in the original article. I really think the Board member concerned should read what was actually written and not what he imagines was contained in the comment. Emotional reactions to submissions - because that is what has occurred here - have no place in science and only serve to bring the journal concerned into disrepute. Hence, I am asking that this submission be reconsidered, possibly by Professor Dorey personally.

Yours sincerely,

Jeremy Dunning-Davies.


Subject: Re: Fw: Final decision on your article from J. Phys. A: Math. Theor. - A/315310/COM/973

Dear Dr Dunning-Davies,

Thank you for your email.Our procedure with all Comments is for them to be initially refereed by a Board Member.  If the Board Member recommends that the Comment be considered further, then a Reply is invited from the original author.  In this instance the Board Member did not recommend further consideration, however I wish to assure you that this is all in line with our procedure and indeed with the information provided by Patrick Dorey.  We consider Comments to be an important forum in the journal and as such, we entrust the refereeing of them to Board Members. I am sorry that you felt the report to be inaccurate, however after further consultation, I must inform you that this decision is final.  I wish you success with publishing your findings in a more specialised journal.

Yours sincerely,

Rebecca Gillan


Dear Miss Gillan,

Thank you for your reply. However, I must confess it only serves to bring J. Phys. A into further disrepute, particularly since the apparent correct procedure does not conform to what Professor Drury originally stated. Also, the Board member's comments simply don't stand up, in the same way that Adler's original article doesn't stand up.

I realise none of this is your fault but this attitude by scientific morons makes you wonder why anyone pursues open-minded scientific investigations.

Yours sincerely,

Jeremy Dunning-Davies.


Final comments by Wilson and Dunning-Davies:

The correspondence Jeremy Dunning-Davies subsequently had with Journal of Physics A is included in full and graphically illustrates, we feel, the attitude being displayed towards independent thought in science today – particularly if that independent thought disagrees, or even appears to disagree, with accepted conventional wisdom. We would, however, point out that the disagreement expressed by us was with some sloppy statistical analysis; the fact that dark matter was involved was really irrelevant to the criticism and possibly shows how vulnerable these people really feel their position to be. This must surely be regarded as a very worrying attitude to find existing at such a level in what is supposed to be scientific publishing.
In all, this has been a disappointing if not predictable exercise. However, it is important that the educated public and professional scientific community continue to raise these criticisms. In the absence of a functional review process, it is even more important for all of us to cast a critical eye on everything we read in journals and the media in general.

Contributed by:

Dr. Jeremy Dunning-Davies and Dr. Thomas Wilson


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