Datta Somnath - Special Relativity, Tensors, And Energy Tensor: With Worked Problems

Special Relativity,
Tensors, and
Energy Tensor

With Worked Problems

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Special Relativity, Tensors, and Energy Tensor

With Worked Problems

Somnath Datta

Formerly, Professor of Physics,
National Council of Educational Research and Training,
New Delhi, India

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Library of Congress Cataloging-in-Publication Data

Names: Datta, Somnath, 1939 author.

Title: Special relativity, tensors, and energy tensor : with worked problems / Somnath Datta.

Other titles: Introduction to special theory of relativity.

Description: Hackensack, New Jersey : World Scientific, [2021] | This book is actually an expanded version of my first book Introduction to special theory of relativity published by Allied Publishers in 1998--Preface. | Includes bibliographical references and index.

Identifiers: LCCN 2020053102 | ISBN 9789811228117 (hardcover)

Subjects: LCSH: Special relativity (Physics) | Electrodynamics. | Electromagnetism. | Space and time. | Relativistic mechanics. | Continuum mechanics.

Classification: LCC QC173.65 .D383 2021 | DDC 530.11--dc23

LC record available at https://lccn.loc.gov/2020053102

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Copyright 2021 by World Scientific Publishing Co. Pte. Ltd.

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Printed in Singapore

This book is dedicated
to
my parents

Snehalata Dutta
Gobindo Lall Dutta

Preface

This book is actually an expanded version of my first book Introduction to Special Theory of Relativity published by Allied Publishers in 1998. The reason I wanted to write another book on the same subject is that I published several articles and papers over the last two decades in the journal Physics Education (on-line since 2013) brought out by the Indian Association of Physics Teachers. These articles were intended to give students and teachers a better grip of some key concepts associated with Relativity, both Special and General. I have incorporated these articles in this book by merging them within its chapters and sections. The reader will find the original articles in the Bibliography. Their references are shown in the next paragraph in square brackets [ ]. My treatments of these concepts are supposed to give additional strength to this book, and constitute a new feature of this book.

I mention some of these features here: An elaborate introduction to tensors and stress tensors; Maxwells stress tensor and conservation of momentum in electromagnetic fields [].

Einsteins two original papers that gave the world the Special Theory of Relativity, and how the well-known phenomenon of electromagnetic induction led him to this theory, have been detailed in my article 1905 Relativity Papers of Einstein []. These two supplementary resource materials are not a part of this book, but they can be downloaded from my website, cited at the end of this Preface.

This book is comprised of four parts divided into twelve chapters. ). I have worked out many innovative problems and exercises. Some of them were designed to remove any doubt centred on relativity paradoxes, like simultaneity, time dilation, and length contraction. In fact my derivation of Lorentz transformation is itself an exercise in this direction. The detailed worked-out problems on Lorentz transformation and relativistic mechanics are intended to strengthen the readers understanding. It is hoped that an undergraduate student studying physics will not only understand and enjoy this part thoroughly but also derive all essential knowledge about Special Relativity from it.

The rest of this book is intended for a reader seeking advanced knowledge, in particular the covariant language, in which advanced texts in Classical Electrodynamics are written. This is where its wider reach is discovered and the journey to General Relativity begins.

The entire .

).

But what is the need for this esoteric trip to four dimensions? Because without it, it would be impossible to look at relativistic mechanics in a holistic manner. Without it how would one explain that energy and momentum together form one unit, the 4-momentum (for which I have).

Pat IV, titled Physics of a Relativistic Continua, has only one very important chapter, namely , dedicated to the energy tensor. We take a brief look at the non-relativistic EoM of a perfect fluid, known as Eulers equation, and extend the lessons to relativistic perfect fluid, which, in combination with the energy conservation of electromagnetic field, completes the energy tensor.

Writing the former edition of this book, and its expansion to this version was a major challenge with manifold obstacles in the way. I owed it to the educational values inculcated at the hallowed precincts of the University of Illinois at Urbana-Champaign, and to the professional ethics of my great teachers, to face these challenges with determination in order to present a true account of the gifts I have inherited from my Alma Mater. My books on Special Relativity and Mechanics are a presentation of this account in a humble way. With deepest reverence and respect I recall some of my mentors: Professor Dillon Mapother (who was instrumental in my changing over from civil engineering to physics), Professor James H. Smith (from whom I learnt Special Theory of Relativity), Professor O. Hanson, Professor G. C. McVittie (legendary authority in General Relativity who taught me an introductory course on this subject), Professor Yavin, and Professor Peter Axel, to name a few.

The memory of Professor James Allen, my research advisor, is etched permanently on my mind. He stood by me during some of my most trying times. To me he was the most shining example of love and kindness.