Special Relativity

A.P. French

• Publisher: CRC Press
• Year: 2017
• eBook ISBN: 9781351988575
• Topic: Physical Sciences
• Subtopic: Geophysics

The book opens with a description of the smooth transition from Newtonian to Einsteinian behaviour from electrons as their energy is progressively increased, and this leads directly to the relativistic expressions for mass, momentum and energy of a particle.

1
Departures from Newtonian dynamics

In experimental philosophy we are to look upon propositions obtained by general induction from phenomena as accurately or very nearly true ... till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

SIR ISSAC NEWTON, Principia (1686)

The relativity theory arose from necessity, from serious and deep contradictions in the old theory from which there seemed no escape. The strength of the new theory lies in the consistency and simplicity with which it solves all these difficulties, using only a few very convincing assumptions ... The old mechanics is valid for small velocities and forms the limiting case of the new one.

A. EINSTEIN AND L. INFELD,
The Evolution of Physics (1938)

WHAT IS IT that you first think of when you see or hear the word relativity? Very likely there will come to your mind the name of Albert Einstein, or the equation E = mc², or a vision of space travelers returning youthful from trips of many years’ duration. This is a well-deserved tribute to the enormous intellectual impact—still effective, more than 60 years after the event—of what Einstein called his special theory of relativity. And the development of this theory by Einstein and others in the years around 1900 is rightly regarded as one of the greatest strides ever made in our way of describing and interpreting the physical world. Yet the basic concept of relativity is as old as the mechanics of Galileo and Newton. It is, crudely speaking, just the assertion that the laws of physics appear the same in many different reference frames. What, then, did Einstein do to make his name almost synonymous with the title of this book? The answer is that he led us to apply the notions of relativity to all our physical experience and not merely to a restricted range of phenomena. In particular, he asserted that processes involving very rapid motions—specifically, motions at speeds of the order of the speed of light—are not to be placed in a separate category. But the unification that he proposed brought with it some remarkable implications. There were consequences that seemed opposed to our intuitions and our common sense, in a way that classical theories were not—the increase of inertia with speed, for example, or the so-called twin paradox. It was such things as this that made Einstein’s_t formulation of relativity so striking and which conferred on it a glamour and a popular interest probably never equaled in the whole history of physics.

We have said that the. idea of relativity existed before Einstein and was embodied in Newton’s mechanics. But it came to be recognized, about 200 years after Newton, that certain observed effects—quite small and subtle ones, for the most part—could simply not be accounted for if one tried to hold on to all the basic features of Newtonian mechanics. Historically the recalcitrant facts, demanding a revision of ideas, made their appearance in electromagnetic phenomena, especially in the propagation of light. It quickly became clear, however, primarily through Einstein’s own work, that all of dynamics, and not merely the specialized field known as electrodynamics, was affected.

It was typical of Einstein, and a sign of his greatness, that he drew conclusions of the most profound and far-reaching kind from a bare minimum of data. Lesser men often attempt the same thing, of course, but differ from the Einsteins of this world in that their grand conclusions or generalizations are usually false. In essence, Einstein constructed the special theory of relativity out of a single proposition, that in every observation of the passage of light from one point to another through empty space the time taken is simply the relative separation of the points divided by a universal velocity c; it depends in no way on any velocity that one’s laboratory may appear to have through space. The development of relativity from this result is not difficult (once Einstein has shown the way) and is logically clear and compelling, and we shall present it in due course. It is a development that begins with optics, proceeds to a revised kinematics, and shows us how we must rewrite the dynamics of particles. But today we can appeal to an immense amount of direct evidence concerning the dynamics of particles traveling at extremely high speeds. This evidence makes it clear from the outset that we must look for a modification of the Newtonian scheme if we are to have an acceptable dynamical description of familiar particles, such as electrons, at all speeds. And in this beginning chapte...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Contents
• Preface
• 1 Departures from newtonian dynamics
• 2 Perplexities in the propagation of light
• 3 Einstein and the Lorentz-Einstein transformations
• 4 Relativity and the measurement of lengths and time intervals
• 5 Relativistic kinematics
• 6 Relativistic dynamics—collisions and conservation laws
• 7 More about relativistic dynamics
• 8 Relativity and electricity
• Epilogue
• A short bibliography
• Answers to problems
• Index