I thank Thee, my Creator and my Lord,
that Thou has given me this joy in Thy Creation,
this thrill in the works of Thy hand.
I have made known Thy glory to men as far as
my limited spirit can grasp Thine Infinitude.
If I have written something unworthy of Thee, forgive it in grace.  ... ”

J. Kepler – “Harmony of the World



This is not a relativity text book.

Nor is it the official presentation of a new theory.

The easiest way of describing this book is to say that it is the record of a voyage, written down by someone who has made an important effort to understand the concepts and consequences associated with the Theory of Relativity.

In some way, it can be said that it is a book of adventures.

Therefore I hope that those, who accompany me in this trip, can share with me some interesting experiences.

In advancing through the different chapters, some readers will think that my thoughts are contrary to the ideas of Einstein. Others will understand that in many cases I leave the “official” path only to reinforce the reasons which reinforce this path.

Some readers, I hope, will agree with my conclusions.

In any case, my biggest hope is that this work will be of use to those who want to understand the behavior of the physical world.


The main objectives of this work can be summed up thusly:

To summarize, I would feel very pleased if, as a result of these lectures, some people begin to accept as reasonable that:


Those who can benefit the most from this book are those individuals who have made their own effort to understand the Theory of Special Relativity or Restricted Relativity, using classic physics textbooks, and find that there are things that are not quite clear in those works.

Those who are first introduced to Relativity through this book may find difficulties in understanding my insistence in posing time after time, from different angles, the same conceptual analyses. This seeming redundancy of argument is because certain conclusions reached do not coincide with the so called “official” interpretation of this formidable physical theory.

At this point it is fitting to clear up that the difficulties in conceptually understanding this theory have given rise to a series of secondary “axioms” that are not only unnecessary, but also difficult an adequate conceptual analysis.

Some of these secondary “axioms” are the following:

As you will see, not a single one of these pseudo-axioms is necessary, in fact, many of them are definitely wrong.

It shouldn’t be surprising, therefore, that the only postulates (or axioms) necessary are the two that Einstein presented in his famous 1905 paper.

Nevertheless, arguing against the aforementioned pseudo-axioms is not easy work. Having been repeated in countless textbooks and talks, formal and informal, they have acquired a privileged status that makes them easy to believe as real axioms of Relativity.

I guess that there might also be the occasional reader who is familiar with the Special Theory of Relativity and does not find conceptual difficulties in it. These readers will think that some of my analyses are pointlessly because relativity equations do not require new interpretations.

I understand the arguments and feelings of this last group of possible readers. It is not my intention to compel them to change their point of view. As I have already said, my thoughts can be useful only for those who feel somewhat swindled by the way in which Special Relativity is explained during teaching or in textbooks.


I have made a serious effort that this book ends up entertaining. To that end equations were minimized, placing greater emphasis on the conceptual discussions, simple numerical examples, and schematic pictures.

Among the different chapters, various themes named “Philosophical Discussion” are introduced. In these asides, I analyze themes that are linked not only to Relativity but to any theory intended to describe the physical world.

These “discussions” can be read independently of the main chapters.

Additional discussions in the form of questions and answers have also been interspersed within several chapters. Many of these questions are taken from actual discussions (the majority from e mails). It is therefore the hope of the author that these questions reflect those which might occur to the reader as they advance through the different analyses.

Lastly, it should be said that this book can not be covered in one sole reading. I believe it inevitable that, in order to adequately incorporate some of the presented concepts, it may be necessary to reread certain chapters as the reader incorporates new developments. The same occurred to the author during the writing of the different subjects.


Although to the reader this section may result to be of limited interest, those, who have written a book, know that writing the acknowledgments is one of the most pleasant and complicated tasks to which the author voluntarily submits himself.

The satisfaction always came from the opportunity to give thanks for some valuable gift given to us.

The difficulty resides in the correct way of expressing each acknowledgment, without committing unfair omissions.

The first acknowledgment is for the “sacred monsters” of science, who bequeathed us the background of knowledge (data) and interpretations (theories or models) with which our insatiable human curiosity is nurtured. In this list, the stars of the greatest magnitude are Galileo, Newton and, of course, Einstein. But I should also include those men who have made the works of these great geniuses accessible to the uninitiated. At this point is my special thanks to Carl Sagan and others such as him, who have taken divulging science as a social obligation.

After them, come the countless teachers (professional or not) who forged the individual that I am at the present time. In this list I wish to include my dear teachers from primary school, the always remembered professors of my high school and University, and the innumerable “philosophical coffee talks” friends. From each one of them I learned something and they are present in many of my personal attitudes as guides and examples.

Nonetheless, the main acknowledgment is for my parents. On top of care, affection, and guidance for my first steps as an individual, in them I identify the first human beings with the capacity to solve problems that exceed, greatly, my own capacity for analysis. They planted in me, genetically as well as spiritually the style that characterizes my way of seeing the world. I remember perfectly my parents introducing me to concepts such as infinity, the size of the universe, and other fascinating subjects of the cosmos or daily activities.

In my only brother, Guillermo, I have always found a speaker at my same level, with whom to discuss some of the concepts that I have presented into this work. To those who want to fight with the concepts of Physics I recommend trying to acquire a brother expert in astronomy. It can be very useful. J

To my own family (wife and three daughters, all marvelous and with their own style) I thank them for their patience and the interest with which they put up with my philosophical discussions.

Sometimes, I even think they enjoy them. J

I would also like to mention many “virtual” friends that Internet brought me, from the moment I decided to throw some of these ideas on the “Web”. The discussions I had by way of e mail have turned out to be very stimulating, and in many cases “required” me to redouble my efforts to understand and develop the concepts here presented.

In this group, and without forgetting all the other that helped me on the path which culminates within this book, I want to explicitly mention Ángel Torregrosa Lillo and Susana Varela Guillot.

My contact with Ángel began by way of an invitation to participate in his relativity forum ( Through many e mails and with notable patience and precision he made me correct and enlarge many pieces until they took the form with which they are presented in this work. In particular, chapter VI as well as the prologue of chapter VII is the results of long discussions over the topics that are discussed in said chapters.

The interaction with Susana is visible in the general format of this work. As an impassioned educator she “obligated” me to correct many expressions and value the use of the word in human communication. It was also she who taught me that in general we write in order to “hear” ourselves. I believe she was right. J

For the final stages of revision explicit thanks go to those who put up with the tedium of reading from the first versions till the final edition. Long discussions with them affect from tiny details to general concepts, so the final result was greatly bettered.

In informal order, these stupendous collaborators were:

Guillermo Crotti (my only brother), Inés Labayén (my dear wife), Rafael Steinberg, Hector Rabal and Norberto Galacho.

Note: For those who have noted that the acknowledgment for my wife is given in two different places, I can say that it is not only in those two places where she is present. J

Nevertheless, I should highlight that, regardless my thanks towards all those who have helped me finish this effort; they are not responsible for any of the possible errors, formal or conceptual, that might be found in this book. That responsibility is mine alone. Their assistance in giving this work its final format in no way includes accepting, in whole or in part, its content. This characteristic makes the collaboration I have received even braver.

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