Revision request for your submission to Annalen der Physik (andp.201600209R1)
Thank you for resubmitting your manuscript "The basic physics of the binary black hole merger GW150914" to Annalen der Physik.
You will be pleased to know that your manuscript has been re-reviewed and recommended for publication pending satisfactory revisions. The reviewer comments are attached below.
Even though the reviewer raised some persistent criticism, his main recommendation is now minor revision. Upon receipt of your proper response and further modified manuscript we plan to take a final decision without a third reviewing round, also in view of the two other positive reports received.
I invite you to respond to the reviewer comments and make the necessary revisions to your manuscript.
To submit your revision, go to http://adp-journal.edmgr.com/ and log in as an Author using your username (ofek) and password. Your submission can be found under the menu item "Submissions Needing Revision".
Please note that when you submit the revised version of this manuscript, you will be asked to upload a zip archive containing the production data that will be used if your manuscript is accepted. See below for more details.
When you submit your revised manuscript, please include a point-by-point response to the reviewer comments in the "Respond to Reviewers" box, including a list of changes made and a rebuttal to any comments with which you disagree. All changes to your manuscript should also be highlighted in the main manuscript file. The deadline for the submission of this revision is 03 Oct 2016.
Once we receive your revised manuscript, we will provide a final decision as soon as possible.
Yours sincerely,
Stefan Hildebrandt, Editor-in-Chief
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REVIEWER REPORT:
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EVALUATION:
Reviewer's Responses to Questions
Please rate the importance of this submission.
Reviewer #1: Should be published in this journal
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Please rate the originality of this submission.
Reviewer #1: Acceptable level of new results
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Please rate the scientific and technical content of this submission.
Reviewer #1: Major inconsistencies or inaccuracies
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Please rate the length of this submission.
Reviewer #1: Concise and correct length
COMMENTS TO AUTHOR:
Reviewer #1: The authors have substantially improved the paper, and responded
satisfactorily to almost all of my comments. There is one point,
however, which they bafflingly refused to consider. They have
essentially combined some fabricated numbers with nonsensical
reasoning that ignores decades of modeling gravitational waves from
binary systems. And they do this to obtain an order-of-magnitude
estimate that is off by an order of magnitude from an estimate they
immediately obtain and claim is more reliable. I cannot recommend the
paper for publication until they have corrected this glaring error.
* Strain at 100km
The authors attempt to place a bound on the distance to the source
using an incorrect order-of-magnitude argument. Even an
order-of-magnitude argument needs some reason (woolly though it may
be) for choosing particular values; this one does not. More
importantly, such arguments also need to remain in the domain where
the concepts actually apply; this one does not.
There are two components of this argument: a pair of numbers giving
the strain h and the radius R at which that strain may be measured,
and a formula for the 1/d_L decrease in amplitude of the waves with
increasing radius. In principle there is absolutely nothing wrong
with this, but they have chosen the numbers in such a way as to
undermine their argument.
1) They give no rationale for choosing the values that they choose
2) They choose them in a region in which the variables are ill defined
3) The 1/d_L scaling does not apply in that region
The authors write in the paper
the strain can be at most h~1 at a radius of the order of the
Schwarzschild radius of the system R~100 km.
I suppose the authors chose h~1 because the strain is defined as the
change in length divided by the unperturbed length, and that does not
make a lot of sense (for contractions) when h gets too close to 1.
But that's all that happens at h~1: the simplistic description the
authors are using breaks down. There are other ways of analyzing
spacetime in those cases that don't just use h. The formulas they
want to use have already broken down. This is not a rationale for
bounding h<~1; if anything it's an indication that the authors should
find a region (presumably at larger radius) where h<<1.
I suppose the authors chose R~100km because the Schwarzschild radius
is a "natural" length scale of the problem in the far field, but they
are not talking about the far field. They are talking about the
system at its most dynamical; general relativity at its most
nonlinear. The very concept of radius is not well defined in this
region. Even if we arbitrarily choose coordinates, parts of the event
horizon can still be located well outside the equivalent Schwarzschild
radius when the peak emission happens. Googling "GW150914 horizons"
and looking at the video on LIGO's own web page shows this.
the amplitude decreases as h~R/d_L
I suppose that the authors say this because they have seen exact
solutions, post-Newtonian calculations, peeling theorems, etc., that
show 1/r behavior. But none of these claim dominant 1/r behavior in a
region of spacetime that is so dynamical that the very meaning of
radius and an outgoing wave is unclear. Anyone who has taken an E&M
course has seen that different regions require different solution
bases, and 1/r is generally not used for an interior solution.
Instead, we find a solution in the interior, and then match at some
larger radius to 1/r solutions. In this case, R~100km can literally
be inside the black holes, which gives new meaning to the idea of
"interior".
We can look for clues to the authors' intentions in their derisive
response to the first round of reviews. I hope it will not be too
distracting that I will be unable to resist the catharsis of a little
reciprocal sarcasm.
Yes, we could of course formulate the argument in the wave zone of
small linearized perturbations, say starting at a distance
R~2000km, with h a small perturabation h~0.1 (the suggested
acceptable "small"). Or at a distance of 2,000,000km, with
h~0.0001. But the conclusion is the same, because the amplitude
decreases proportional to the inverse of the luminosity distance
1/d_L (which certainly holds in the wave zone)!
I'm not sure if the authors are trying to insult my intelligence, or
just give me a laugh by combining circular reasoning with a straw man
argument. They can divide one number by 10 while multiplying the
other by 20, and arrive at the same order-of-magnitude product?
Bravo. They can even throw in factors of 1000 and 1/1000? Well done
indeed. They've established that they know how multiplication works.
Seriously though, that statement exposes what the authors are actually
doing: they are adjusting R and h as necessary to arrive at
approximately the answer they want. But they have not indicated why
any one of these numbers should take on the given values.
Ignoring my distaste for ever using the bound h~1, why should that
value only occur at the Schwarzschild radius? Why not bound h by 1 at
the wave zone (R~2000 km)? Is it because this would increase their
result so much that the authors would have to admit their estimate is
silly? Thorne [1980 Rev. Mod. Phys.] suggests 10M as the boundary of
the "strong-field region"; why not bound h by 1 at R~1000km?
Alternatively, we can take the authors' most recent tack of abandoning
bounding, and go to estimates. But then how would the reader know
that h should only be "small" (h~0.1) at R~2,000 km? Why not
"super-duper small"? How about h~10^{-6} at R~2,000 km? In that
case, we would get d_L~65 kpc. Why is that not the estimate, as long
as we're just making up values? This has as much motivation as the
authors provided for their numbers.
In the following paragraphs, we obtain a much more accurate
distance estimate. This more accurate estimate shows that the
luminosity distance d_L is about an order of magnitude larger than
given by the first cruder estimate. This demonstrates that h is
only about ~0.1 in the system zone. So bounding h<~1 in the system
zone is conservative and justified in this case.
Oh I get it now. Arbitrarily making up numbers and misusing a scaling
law is justified if the result comes out to be wrong by only one order
of magnitude compared to a more accurate estimate. Solidly reasoned.
To summarize, we do not give wave-zone calculation, because (a) it
does not lead to a different conclusion, and (b) we immediately
give a more accurate estimate.
Clearly, (a) only the authors' straw man fails to obtain a different
conclusion, and (b) there's one more reason this is silly. There
would be merit in this simpler estimate if it were properly
constructed; it currently is not.
Again, I see no reason that this paragraph should not simply be
removed. If they wish to keep it the authors, at the very least, will
have to come up with (1) an expressible rationale for choosing a
particular value of h that doesn't just rely on the breakdown of the
overly simplistic mathematics of h, (2) an expressible rationale for
choosing a particular value of R that is relevant in the chosen region
of spacetime, (3) values of h and R in a region where those quantities
are reasonably meaningful, and (4) any credible argument for dominant
1/r behavior in the region near R when the spacetime is highly
dynamical. But I really suggest the authors just drop the paragraph.
* Proof in observational astronomy
The text has been reworded sufficiently so that it is no longer
objectionable, but I am concerned that the authors have not taken the
lesson to heart. This does not require any action or response from
them, but I would appreciate it if the authors would consider what I
have to say, in the context of a paper that was previously riddled
with claims to "proof".
We do maintain that in any argument, assumptions must be made;
I obviously agree that assumptions must be made in any argument. And
of course we don't need to explicitly list every assumption during
every attempt at persuasion. But framing an argument as if it were a
formal proof requires a higher standard. If you can't meet that
standard, just don't frame it as such.
More specifically: even in informal persuasion, if you use argument by
contradiction, you cannot pull out just one of the assumptions that
went into your argument and say that's the one contradicted. It's the
combination of all your assumptions that is wrong, and logic gives you
no way to decide the incorrectness of any one assumption. Claiming
otherwise is a fallacy.
for example a student learning Newtonian mechanics "proves" that
the external gravitational field of a spherically symmetric object
is unchanged if all the mass is concentrated at the center.
But a student "proving" the shell theorem starts from a 1/r^2 force
law, does an integral or two, and arrives at the result fully
conscious of the fact that it depends on calculus and the assumed
force law. On the other hand, the authors have constructed some of
the most complex scientific instruments ever created, took a lot of
noisy data, did a bunch of filtering that (while presumably
reasonable) was too obscure to adequately specify in this paper,
assembled a towering series of hand-wavy interpretations of features
in that data, resting on numerous approximations, and then proceeded
to draw out one conclusion as if it were the unavoidable result of a
three-line computation in formal logic. There's a bit of a
difference.
So it's clear from context that our "proof" is contingent
If you ever again find yourself insisting that a "proof" is contingent
on a list too long to be listed, it should not be referred to
(explicitly or implicitly) as a proof.
If you ever again place scare quotes around the word "proof" when
defending their use of a phrase (like "reductio ad absurdum") that is
only used in contexts where that word actually means something, you
should probably re-evaluate.
I would advise you to instead find a thesaurus and take your pick from
related but more accurate words, such as "argument", "evidence",
"consistent", "corroborates", "suggests", or "favors".
--
Dr. Stefan Hildebrandt, Editor-in-Chief
Annalen der Physik
http://adp-journal.de/
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