The review process provides a level of quality control that insures that published papers are correct and of interest to the scientific community. Since reviewers are themselves scientists with busy schedules, and being a reviewer provides no compensation aside from the satisfaction of being a good citizen, editors often find it difficult to get the best people for the job. This has led to an increase in desk rejects by the editor, which avoids wasting reviewers' time on manuscripts that will most likely not be accepted. The review system is frustrating to all parties involved.
I've been involved on all sides. As an editor, I took lots of grief from angry authors. In one case, I got a phone call from an irate author whose paper I had rejected. He lectured me that as an editor of a prestigious journal decades prior, he would use at least one of the reviewers that the author had recommended. Why had I not done so? Because the review process is anonymous, I could not tell him that I used two of the three physicists that he had suggested, and they both recommended that the paper be rejected. As a compromise, I selected his third choice of reviewer, along with yet another one. Again, they all rejected the paper. I could have avoided the next phone call and the indigestion that followed if I would have disclosed the fact that I had chosen at least one of his recommendations. But I could not.
On another occasion, one of my colleges refused to act as a reviewer on a paper for which he was perfectly suitable. That same colleague had an issue with one of his papers (not to my journal) where he needed my help, so I used it as leverage to get him to act as a reviewer for me. There are all sorts of behind-the-scenes dynamics that are not always obvious to authors or reviewers. The bottom line is that the process is far from perfect, which brings disdain from authors who are unhappy with the results.
I am writing this post to describe an example of a rainbow amidst the storm.
The American Journal of Physics is one of the coolest Physics publications on earth, so I read every monthly issue cover-to-cover. There are always a few articles in each issue that surprise and delight. They often point out subtleties in topics that you might think mundane, and bring insights that have been missed by the research community.
Being an author of a couple papers in AJP over the last two years, I have found the review process to be excellent. The reviewers are knowledgeable and seem to spend lots of time trying to understand the work. The exchanges are a real learning experience, and all parties are flexible -- admitting mistakes and savoring the process. Here I describe an example of my experience with a paper that will be appearing in December (here is a link to the preprint).
The editor notified me that my paper had mixed reviews:
"Attached you will find copies of the reviewers' reports on your manuscript "Length as a Paradigm for Understanding the Classical Limit." Though the reports differ in recommendation, it is the content of the reports that is more important than the recommendation per se, and all three reviewers seem to be focusing on the same (or almost the same) issue: The justifiability of your model for what you call length. It will be necessary for you to address this issue in a revision. There are additional detailed corrections and suggestions that should also be carefully in a revision.
If you wish to revise your manuscript along the lines indicated, we would continue its editorial consideration once it has been resubmitted using the procedure indicated on the AJP website. If you do resubmit, please indicate in a single cover letter how you have responded to the various comments of the reviewers. DO NOT send separate replies for each reviewer.
Thank you for your interest in the American Journal of Physics."
The first thing that caught my eye was the fact that this was not the usual form letter used by most journals. The editor had carefully read the reviews and noticed some common criticisms. I eagerly dove into my revisions, finding that the reviewers' questions and confusion were the result of deficits in my paper. I knew what I was trying to say, but my obtuse presentation of the material was only made obvious by their comments. Most importantly, responding to the reviewers forced me to think more clearly about the physics. As a result, I gained insights into my own work when making the revisions, increasing substantially the quality of presentation.
Exchange With Reviewers
Particle in a Box
I will focus here on the common complaint made by all the reviewers, which centered on my use of the particle-in-a-box model. Here are their complaints:
REVIEWER #1
My only concern is the basic assumption used to model the ``quantum'' systems. The author is assuming the quantum system is inside a box with hard walls (it uses the infinite well model to derive the wave-function of one electron, and then generalizes it to non-interacting particles). While this is a simple an intuitive model to work with, it is not clear that the results would carry on with more realistic potentials that might have different boundary conditions.
REVIEWER #2
In the work, the focus lies on the electrons of a material and the nuclei are taken as a scaffolding for them, which is the usual approach for solid state physics. Yet, the wavefunction for the entire ruler will truly include the atoms as well. I would expect that the length of the ruler as calculated through this procedure will change when including these additional fermions, while I reality the length of the rod will remain the same. If this is so, it would jeopardize the numerical results in this work (although not its method)
REVIEWER #3
It
is also strange the definition of the length of an object as the sum of the
densities of the electrons confined in that potential, like the example of the
particle in the box. The length of a real material should depend on the
properties of the nuclei as well as of the electrons.
My Response:
Since all the reviewers brought up a similar point, I responded to them as a group. Here is the verbatim response:
We interact with materials either by looking at them with our eyes (light scattering from electrons) or touching them (repulsion between electrons in the material and within us). I believe that we all would agree that what we ``see" are the electrons, though their density does indeed depend on the presence of the nucleons. So two materials with the same electron density but different nuclear positions would appear the same. The mass, of course, is dominated by the nucleons, but we are viewing/touching the electrons when determining the length. The length would be different if we did scattering experiments that are tuned to only probe the nucleons, but on the scale of human senses, we see only the electrons. In either case, the lengths determined in these two ways would be similar for multi-atom quantum systems.
The positions of the nucleons are well represented by the Born-Oppenheimer Approximation, where the nuclear equilibrium positions are determined by the configuration with the lowest total energy. Some of the electrons are involved in stabilizing the system -- which can be viewed as chemical bonds -- and in materials such as metals, the rest of the electrons are delocalized over the bulk material. In the absence of defects, bulk metals appear smooth so each conduction electron moves approximately freely within the metal and encounters a large barrier at the edges.
This picture roughly holds for all materials and uniform electron densities are found is a variety of systems with delocalized electrons modeled by particles in a box. These include small molecules such as the polyenes, as modeled by Kuhn in the 1940s, to metals as described in solid state textbooks, to nanoparticles that straddle the classical/quantum divide as recently reported by Scholl.
I would thus argue that the particle in a box is a good model that roughly holds well for many systems. Much more sophistication is required to deal with the nuances. I therefore believe that using the particle in a box model contains the correct physics that is assessable to a student. Taking into account the reviewers' comments to explain this to the reader, I have added a third paragraph to Section III.A that reads:
"Models of materials with non-interacting electrons in a box roughly predict the electronic properties of small molecules such as the molecular class of polyenes,\cite{kuhn48.01} describe metals as found in solid state textbooks\cite{OpenStax20.01} and accurately portray the quantum to classical transition of nano-particles.\cite{schol12.01} This shows that the effect of the nucleons on the electrons can be roughly taken into account with a box that confines the elections within. We will thus model typical materials with uniform electron density as non-interacting electrons in a box. The reader should keep in mind that this is a first step in modelling materials in which electrons are delocalized. Later we treat materials made of such units that are ``pressed" together. Then, the electrons are localized within domains rather than over the full material. For simplicity, we will treat only one-dimensional systems. Other potentials can be treated in the same way, but this exercise does not result in significant-enough insights about length itself to make it worthwhile to treat in this paper."
The reviewers we satisfied with my response. Here are excerpts from their second set of comments:
REVIEWER #2 - Second Response
I'm particularly satisfied with the argument to not include the
nucleons in the the total wavefunction. I've learned a new insight
here, using the Born-Oppenheimer approximation. Also, I think the
added paragraphs to section III add to the quality of the story.
REVIEWER #3 - Second Response
The author presented an improved manuscript that discusses the
difficult concept of quantum length. The language in the response
and the changes in the text greatly improved the manuscript.
Definition of Length
REVIEWER #3
This reviewer thought that my paper was wrong and should be rejected on the basis that I defined the length in a certain way that was arbitrary. In the reviewer's own words:
It
is my opinion that the manuscript is not technically correct as it starts with the definition of
length of rod in terms of its uncertainty in the position.
The reviewer continues with technical details. This comment led me to see that I was unclear in my presentation. I responded with:
Your major criticism of this manuscript is with the ``definition of the length" and your argument against this definition is based on the fact that the coefficient $\sqrt{12}$ would change if the material were not uniform. The original version treated only the uniform classical rod as the length element. In the revised manuscript, an appendix describes how a non-uniform classical rod is treated, and is referred to in the main text. Your argument is analogous to stating that the Pythagorean theorem can't be right because the expression would depend on the shape of the curve along the hypotenuse. As with Pythagoras, where the length of the curve is obtained by dividing it into infinitesimal straight sections, so too the classical length is computed as the sum over uniform segments. In retrospect, the original manuscript did a horrible job by neglecting this description. I believe that using an appendix eliminates confusion yet maintains the flow of the narrative.
I have also added a couple paragraphs, as described above in the general section, which argues for the ansatz for the quantum length, a regime where it is no longer possible to subdivide a material without changing its properties. I hope that these two major revisions remove confusion and makes you comfortable with the length expression that results from applying translational invariance and classical correspondence.
In response to my revisions, the reviewer adds:
The added appendix lets the reader know that there are other
definitions that would converge to the proper classical limit. I
would like to see incorporated in the beginning of manuscript the
statement that the author made about how theories are developed.
This would be very helpful for the readership to explain how one
should approach making comparisons between new theories and their
classical limits. Incorporating these ideas on someone’s teaching
can help students navigate phenomena they are seeing for the first
time while relating them to things they are familiar with. These
ideas are incorporated in the Lessons Learned section, however,
helping the reader have this framework at the beginning of the
manuscript can guide the reader on understanding the assumptions
made, the development of the concepts, and finally understanding
the conclusions in the end.
It is my opinion that the manuscript might be published in the
present form, but it can still be improved by incorporating the
four points on theory developed in the introduction:
1. Setting the physical constraints. Here the length is required to
be translationally invariant and to give the correct classical
result.
2. Choosing the simplest ansatz that meets the constraints. The
uncertainty happens to meet the translational invariance criteria
but the length is NOT ad hoc defined as the uncertainty.
3. Demanding that the quantum theory in the classical limit gives
the classical result. Here, the quantum length and classical length
converge in the many-particle limit and for one particle in the
limit of it occupying the highest-energy state.
4. Investigating the Consequences. Here we apply the ansatz to
rulers and measurement.
In addition to being satisfied with my revisions, my comments to the reviewer led them to conclude that the response I had directed at the reviewer in my rebuttal was so useful that it should be added to the paper. This was a great idea, and an example of what I was thinking when I was writing the paper, but something that I had not verbalized. This gave me the opportunity to carefully craft what I think is an important takeaway message of my paper.
Conclusion
There are many other useful exchanges with the reviewers that would take too much time to summarize here and would add too much length to this post. So instead, I have uploaded all the files with the reviewers' comments and my responses, to which I provide links below. The end result is that I got great advice, which led to a much better paper not only in the presentation style, but in substantive additions to the content. More importantly, I feel a deep kinship with these reviewers, who bared their minds to me in a frank dialog that gave me a more nuanced understanding of the topic. I am indebted to these individuals who sacrificed their valuable time without compensation, other than to savor the satisfaction of learning about and understanding the subtleties of our world.
