Conceptual Relativity
by Marcelo Alejandro Crotti (

A site for people who know that lengths and intervals may suffer alterations,
but... does not understand why

This site contains the English version of a revolutionary, but very easy to read, book, devoted to show that Relativity is not a theory only understandable for very few specialist. By reading the almost "equations free" chapters, the reader will be surprised verifying that common sense can be again at the center of the physical scenario. A place from where it should never been removed.

Remark: The spanish version of this book is available at


Relativity is a theory developed to describe interactions in the physical world through mathematical equations.

This theory can be divided into two main branches:

The first describes the cosmos, in the large scale as in the small one. In order to meet its goal, Operational Relativity gives us a series of equations which reflect, through mathematics, the behavior of the physical world.

In few words, Operational Relativity is a work tool and, as such, it is used routinely in science and technology.

The second branch is very different. Studying Conceptual Relativity in depth implicates, inevitably, invading the fields of Philosophy.

Attempting to understand Relativity is attempting to understand the world around us, not by way of equations, but rather by way of concepts.

So we can define Conceptual Relativity not as a tool, but rather as an object of study.

We can think of the two branches as twin sisters with very different characters...

Operational Relativity is the one that has triumphed in the world of science… The physical world behaves just as is shown by relativity equations. Their predictions are excellent.

But…, the Conceptual relativity sister has not reached the same level of success.

The Operational sister is extroverted; she likes the show and the great public.

The Conceptual sister is introverted. Not much is written about her life. In fact, there are many authors who hate her because they say she is difficult to socialize. Every time she arrives on the scene, some kind of problem comes up. This sister behaves herself like one of those bothersome children who is always asking why? Eventually this tires the answerer who ends up responding badly and telling the child to be quiet.

The conceptual sister is so difficult to introduce to society, such that almost nothing is written about her. Physics courses pass very quickly from the concepts to the equations. In general, the professor goes directly to calculations just when the discussion began to be entertaining for the student and uncomfortable for the professor.

As a result, by not socializing, the Conceptual twin sister has remained in her infancy. Paraphrasing the respective histories of the relativity twins, we could say that we have sent the conceptual sister on a trip, so that she doesn’t bother us during routine work. Because of that, her clocks have moved more slowly.

It is a simple matter to verify that the Conceptual sister has not reached maturity: We are still asking the same questions that were asked 100 years ago …

In the simplest words, Operational Relativity responds to the Whats, and Hows of nature. The more timid sister tries to respond to the Whys.

Even though it doesn’t appear so, she is the truly revolutionary sister.

Inside this simplified panorama this work has been conceived to grant Conceptual Relativity her adulthood. All of the analyses and developments, which will be presented here, are meant to validate relativistic equations from the conceptual point of view.

The trip is not easy. We are walking along it, from 100 years ago to the present, without apparent progress.

But I hope the trip will be amusing. Additionally, the path here presented opens the door to other paths which are impossible to reach if we go away from the lane of explanations.

Remark: If the reader expected that, by speaking of the two branches of relativity, it would be Special Relativity and General Relativity, the reader can already appreciate that the focus of this work is a little bit different from that of conventional Relativity books.


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--- Special Relativity easy to understand from a classical point of view --