Lorentz transformation from an elementary point of view – from blogging to science publishing

This morning I received the following email

Your submission “Lorentz transformation from an elementary point of view” (MS #3302) has been published to Electronic Journal of Linear Algebra.


Want to maximize readership? Improve the Google rank of your submission by putting its title, formatted as a link, on your personal or departmental webpage at your institution.

Thank you,

The Editors

Electronic Journal of Linear Algebra

I checked, and indeed, there it is for everybody to read:


I am writing this post not exactly in order “to maximize readership and to improve the Google rank“. I am writing it because this particular paper has an interesting history related to …. blogging. I will describe this story now.

It all started when on April 1, 2014, on my Polish blog, I have made a post entitled “Zwłoki Ridriguesa” – “The corpse of Rodrigues”. My post, with a funny title, was about a paper that I received for reviewing for a journal. There were two authors, both of them Turks, and the paper was dealing with the Lorentz group (the symmetry group of Einstein’s Special Relativity Theory).
At that time I was working on my book ” Quantum Fractals From Heisenberg’s Uncertainty to Barnsley’s Fractality” that appeared in print at the end of that year. While my book was about quantum fractals, quantum measurements, quantum jumps, there were also important parts there dealing with the Lotrentz groups that, for some mysterious and not yet understood reasons plays a role in quantum measurements of electron and proton spin. There are also mysterious connections with the phenomenon of relativistic light aberration. In all these phenomena the Lorent group plays an important role. Here is an extract from the index of my book:

matrix, 68, 94
transformation, 29, 45, 54, 66, 89,
92, 103, 110
Lorentz boost, see boost, Lorentz
Lorentz group, see group, Lorentz, 53
orthochronous, 46
restricted, 46–48, 50, 314
Lorentz matrices, 28, 40, 45, 52, 96,
101, 110, 126, 130
distance, 43

So I got interested in the paper of the two Turkish mathematicians,
Mustafa Özdemir of Akdeniz University and

Melek Erdoğdu of Necmettin Erbakan University in Konya. But, at the beginning, I was very suspicious. No so about Turkey, but the authors were quoting some “Rodrigues formula” and, since 2012, I was not anymore in friendly relations with Rodrigues. When I started studying the paper I realized that there Rodrigues was from the year 1884 – not the same as my ex-friend. So I started reading and checking the formulas in the paper one by one. After two weeks I have obtained, what I thought, better formulas. I was posting about my progress with improving the Turkish paper on my blog, and soon there were quite serious discussion about the subject, with lot of important observations and contributions from my readers, mainly from “TICHY” and “BJAB”. The end result of all that was that I have suggested several improvements to the paper (“On the Rotation Matrix in Minkowski Space-Time” by Mustafa Özdemir and Melek Erdoğdu, and that I coauthored a separate paper on the subject using different methods – “A Comment on ‘On the Rotation Matrix in Minkowski Space-time’ by Ozdemir and Erdogdu“. It all started and developed thanks to the blog.

It took us eight months of intensive email exchanges. We fought because I am a physicist and he is a mathematician. We have different ideas about what is evident and what not, what is simple and what is complicated, what can be considered as a “proof”. But we did it. In our paper we did not write even 10% of what we knew. Jerzy, my coauthor, decided that we should publish it all, and that we should aim at writing it using only elementary methods that can be understood by a student taking an elementary linear algebra course. Jerzy took almost all the burden of writing it all up. When it was all done we have to face the problem of finding a publisher. First we tried Journal of Geometry and Physics. We got the reply

the Journal of Geometry and Physics is devoted to the publication of top-quality research papers whose topics lie in the interface between geometry and modern theoretical physics.

We think JGP it is not the correct recipient for papers like yours. Therefore, we regret we will not be able to publish your paper.
This is not a rejection; rather we shall consider your paper as withdrawn

That was not a surprise. If you write your paper in such a way that everything is clear and everybody can understand what you are talking about, then many journals will refuse publishing it even without sending to pear review – if you can write clearly, it means you are not a real top scientist!
Then we tried Acta Applicandae Mathematicae – with result:

The paper is outside the scope of Acta Applicandae Mathematicae, being unsuited to its broad mathematical readership. The authors may wish instead to submit the manuscript to a more specialized journal.

Our next try was Electronic Journal of Linear Algebra. That proved to be the right choice. From there we received encouraging referee reports including

The paper has been meticulously written in whole. Each detail is studied. Authors obtained important results…. the paper is very interesting and elaborated. The main idea and motivation of this paper is very good.

This is a well written and elegant paper. It a presents some definite results

I find this approach interesting and relatively novel. Moreover, the paper is clearly and consistently written without using specialized terminology or advanced methods to present some complicated mathematical problems of the Lorentz transformation. Standard textbooks on linear algebra and calculus should be enough to understand this formalism. Thus, I believe that the present article can be useful and inspiring for a broad audience.

So our paper was finally accepted for publication. But very soon we have found that the referees did not really read the paper deeply enough! Sarah, the copy editor for the journal, wrote us about her doubts concerning one particular formula. And indeed, it was bad, very bad. Fixing this error proved to be equivalent to rewriting one of our “Theorems” and introducing quite a number of additional changes in order to avoid misunderstandings. Now all of it is in the past, and the paper is out for everybody to read and to criticize!

In the meantime, while working on this paper I received email from Ivailo M. Mladenov, Senior Research Fellow at Institute of Biophysics Bulgarian Academy of Sciences

Dear Professor Jadczyk,

It is by some chance that I have
to came across your paper entitled


There I have seen formula (43) which is the main
result of your paper without even mentioning that
it appears almost 10 years ago as (17) in


I do not think that this is the right way
for doing science.

Sincerely yours,

Ivailo Mladenov

web: http://www.bio21.bas.bg/ibf/dpb_files/im/Mladenov.htm

And indeed, I was not aware of this paper when submitting for publication our paper. Today the first thing we often do when starting any research is searching Internet. But even with all the searching capabilities available we often miss something that did not make its way to the top ten or twenty of Google search pages. I checked and indeed, the paper by Dimitrov and Mladenov contained several results that coincided with those in our paper, though obtained in a different way. We are quoting Dimitrov and Mladenov paper in our new, “elementary” paper. I hope they are happy now.