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E=mc² is known as the most famous but least understood equation in physics. This two-volume textbook illuminates this equation and much more through clear and detailed explanations, new demonstrations, a more physical approach, and a deep analysis of the concepts and postulates of Relativity. The first part of Volume I contains the whole Special Relativity theory with rigorous and complete demonstrations. The second part presents the main principles of General Relativity, including detailed explanations of the bending of light in the neighborhood of great masses, the gravitational time dilatation, and the principles leading to the famous equation of General Relativity: D(g) = k .T. The most important cosmological predictions are then described: the Big Bang theory, black holes, and gravitational waves. Plentiful historical information is contained throughout the book, particularly in an ending chapter depicting the scientific and epistemological revolution brought about by the theory of Relativity. Volume II progresses into further depth than Volume I, and its scope is more extended than most introductory books on Relativity. It includes the affine connection, the geodesic equation, and an introduction to cosmological models. The mathematical tools dedicated to Relativity are carefully explained for those without an advanced mathematical background (tensors, Lagrangians, covariant derivative). Both volumes place an emphasis on the physical aspects of Relativity to aid the reader’s understanding and contain numerous questions and problems (147 in total). Solutions are given in a highly detailed manner to provide the maximum benefit to students. This textbook fills a gap in the literature by drawing out the physical aspects and consequences of Relativity, which are otherwise often second place to the mathematical aspects. Its concrete focus on physics allows students to gain a full understanding of the underlying concepts and cornerstones of Relativity.

More information can be found at: https://www.relativitybruma.com/

**Volume 1:** 1. Relativity of Time and Distance 2. The Lorentz Transformation 3. Other New Kinematics Laws, Causality and Accelerated Trajectories 4. The Next Revolution: Dynamics 5. The Energy Revolution: E = MC²γ and Its Consequences 6. Introduction to General Relativity 7. Cosmological Consequences 8. Epilogue: A Scientific and Epistemological Revolution 9. Solutions to Questions and Problems

**Volume 2: **1. Steps Before the Lorentz Transformation 2. The Lorentz Transformation. the New Metric and Accelerated Objects 3. The Relativistic Laws of Dynamics 4. Introduction to General Relativity 5. Important Consequences 6. Introduction to Cosmological Models 7. Further Axiomatic Considerations 8. Answers to the Questions and Exercises

### Biography

Paul Bruma is a French engineer who graduated from Institut Polytechnique - Telecom, Paris. This curriculum includes a broad program in mathematics and physics, equivalent to a Master’s degree in science. After a career with the international telecom equipment manufacturer Alcatel-Lucent (former Bell Labs), Paul Bruma resumed physics studies, which was his favorite discipline as a student. Regarding Relativity, Paul Bruma found that most text books lack explanations and are very mathematically oriented. This explains why this subject appears quite complicated to students, and many frequently zap from one book to another in search of the missing explanations in their text books. Relativity being an essential subject, Paul Bruma took up the challenge of making a book that contains all explanations and in a manner which is as accessible as possible while always being absolutely rigorous. This induced him to adopt a more physical approach than most authors. In his previous career in the high tech industry, Paul Bruma had many opportunities to write technical documents explaining complex subjects and to train teams. In this domain, if technical specifications are not written in a clear, detailed, step by step and unambiguous manner, the implementation teams won’t work effectively and the outcome will likely differ from what was intended. In contrast, academic authors often consider that students should fill by themselves some missing steps or explanations as part of the pedagogical process. Paul Bruma believes that this method is not the best one for Relativity because it is a domain where common sense often misleads.

"The beginning of last century witnessed two major revolutions in the physical sciences which changed profoundly our perception of space and time and our views on the structure of matter. They are known as The Theory of Relativity for the first, and Quantum Mechanics, for the second. They both have a well deserved reputation of complexity and this has scared people away. Only specialised professionals dared to study and understand them. Yet, both are omnipresent in our everyday lives. The tiny chips which form the heart of our smartphones could not be designed without quantum mechanics and our GPS would be grossly inaccurate without the theory of relativity. Maybe it is time to try to demystify these theories, make them accessible to those among the younger generation who are interested, well motivated, and have followed a good science course at High School.

This book tries to meet this challenge for the theory of Relativity. By 'demystifying' I do not mean a kind of vulgarisation which avoids the difficulties by offering more or less convincing plausibility arguments. The ambition of this book is to explain every point by presenting a rigorous and complete derivation. It starts from first principles, sets the axioms, and develops the theory step by step in a fully deductive way. Every assumption is solidly anchored in experimental results.

The book contains two volumes. In the first we find the general principles and the main results, first for the special theory, (chapters 1 to 5) and then for the general theory of relativity (chapters 6 and 7). More advanced points are left for the second volume. The book is not "easy" and the reader should follow every step carefully and repeat the calculations, but the end result is highly rewarding. At the end he, or she, will have a very good working knowledge of this very beautiful theory. A great help is provided by well chosen problems and exercises which we find at the end of each chapter. I strongly advise the reader to try hard to solve them. The solutions can be found at the end of the second volume, but it would be a mistake to look there directly for the answers.

There exist many excellent books on the theory of relativity but, contrary to most of them, the author of this one does not require the reader to have a background in physics and mathematics beyond what one can reasonably expect from a good high school graduate. The result is amazing. Incredible as it may sound, the author wins his bet. He shows that the theory of relativity is not "difficult". It is fully accessible to the kind of readership he set to meet.

It is the book I wish I had 65 years ago, when I finished high school."—Professor and Researcher Jean Iliopoulos, recipient of the 2007 Dirac Prize

"I certainly think the book is very worthwhile. It fills a gap in the literature, in that special relativity in itself is not so much taught in the curriculum, undergraduate or graduate, as it is typically discussed in a more summary form in other courses. In the courses where it is more extensively used as a tool, the physical consequences are not brought out so much as the technical and mathematical aspects. Your book makes the physical consequences concrete and goes beyond the simple demonstrations to allow a fuller understanding of the underlying circumstances, e.g. the way the clock synchronization requirement brings about both time dilation and length contraction."

—Ryan Rohm, University of North Carolina at Chapel Hill

"An excellent approach, and a thorough treatment of the subject."

---Michael Dine, Professor at the University of California, Santa Cruz Institute for Particle Physics (SCIPP)