1st Edition

Introduction to Relativity Volume II In-Depth and Accessible

By Paul Bruma Copyright 2023
    286 Pages 62 B/W Illustrations
    by CRC Press

    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.

    Volume II contains, notably:

    • In Special Relativity: complementary explanations, alternative demonstrations relying on more advanced means and revealing other aspects. Further topics: accelerated objects and the Relativistic force, nuclear reactions, the use of hyperbolic trigonometry, the Lagrangian approach, the Relativistic Maxwell’s equations.
    • In General Relativity: tensors, the affine connection, the covariant derivative, the geodesic equation, the Schwarzschild solution with two of its great consequences: black holes and the bending of light; further axiomatic considerations on time, space, matter, energy and light speed.
    • In Cosmology: the FLRW Metric, the Friedman equation, the cosmological constant, the four ideal cosmological Models.

    These subjects are presented in a concrete and incremental manner, and illustrated by many case studies. The emphasis is placed on the theoretical aspects, with rigorous demonstrations based on a minimum set of postulates. The mathematical tools dedicated to Relativity are carefully explained for those without an advanced mathematical background.

    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.

    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


    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 theory of Relativity, like Quantum Mechanics, has a well-deserved reputation of complexity and this has scared people away. 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. By 'demystifying' I do not mean a kind of vulgarization 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 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 they will have a very good working knowledge of this very beautiful theory. A great help is provided by well-chosen problems and exercises.

    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