Table Of ContentUNDERSTANDING
RELATIVITY
· Stanley Goldberg ·
Birkhauser
Boston • Basel • Stuttgart
UNDERSTANDING
RELATIVITY
Origin
and Impact
of a
Scientific
Revolution
Library of Congress Cataloging in Publication Data
Goldberg, Stanley.
Understanding relativity.
Bibliography; p.
Includes index.
1. Special relativity (Physics) 2. Science-Methodology.
3. Science--Histoty.
I. Title.
QCI73.65.G65 1984 530.1'1 83-22368
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Goldberg, Stanley:
Understanding relativity / by Stanley Goldberg.
-Basel ; Boston; Stuttgart; Birkhiiuser,
1984.
ISBN-13: 978-1-4684-6734-5 e-ISBN-13: 978-1-4684-6732-1
DOl: 10.1007/978-1-4684-6732-1
Copyright © 1984 by Birkhauser Boston, Inc. All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise, without prior permission of the copyright owner.
Softcover reprint of the hardcover 1s t edition 1984
To my mother, Sarah Belle Talisman Goldberg.
And to Frank Weissman, Ollie Loud and Trevor Coombe:
Though miles, even light years apart, they have kept their
eyes on the same star:
The Dignity of People.
Contents
Preface
Xl
Acknowledgments xv
I. THE CREATION OF THE THEORY OF RELATIVITY
1
1. Science, Logic, and Objectivity 5
The Role of Mathematics and Other Formal Systems in Science 5
The Case of Euclidean Geometry 7
The Case of Natural Numbers 10
The Case of Free Fall 12
The Aristotelian Analysis of Motion 14
The Galilean Analysis of Free Fall 21
Belief as a Culrural Phenomenon 33
Objectivity and the Social Institutions of Science 36
Science and Technology 38
2. The Rise and Fall of the Mechanical Wodd View 41
The Seventeenth Cenrury 42
The Evidence 48
Newton's Axioms and Definitions 51
The Application and Consequences of Newton's Laws 56
Newton's Theory of Measurement 68
The Galilean Transformation Equations 73
The Classical Principle of Relativity 80
Vll
Contents
The Search for the Absolute Frame of Reference 82
3. Einstein's Special Theory of Relativity and Its
Consequences lO3
The Special Theory of Relativity lO4
The Postulates 104
Simultaneity 110
The Relativity of Simultaneity 113
The Order of Events and Causality 115
The Relationship of Einstein's Theory to Lorentz's Theory 116
Time Dilation and the Relativity of Simultaneity 119
Length Contraction 124
Mass 131
4. Further Consequences of the Heuristic Nature of the
Special Theory of Relativity 151
Mass and Energy 153
The Clock Paradox 159
Four-Dimensional Analysis 162
5. The General Theory of Relativity 169
II. THE EARLY RESPONSE TO THE SPECIAL
THEORY OF RELATIVITY, 1905-1911 179
6. When a Hundred Flowers Bloom: The Gernian
Response 185
The Contributions of Max Planck 189
The Rigidiry Paradoxes 191
Wave and Group Velocity 196
7. As If It Never Happened: The French Response 205
Henri Poincare 206
The Principle of Relativity 208
Poincare and Second Order Theory 2lO
The Theory of Electrons 211
Poincare's Vision of a Good Theory 212
Simplicity and Induction 212
Flexibility and Gradualism 213
Naturalness and the Increase of Hypotheses 214
Poincare's Silence and Einstein's Theory 215
Other French Response 216
Aftermath 218
V111
Contents
8. Defending the Ether: The British Response 221
The Tradition of British Ether Theory 221
Oliver Lodge 223
The Mechanical Ether 226
The Introduction of Relativity Theory 230
Conclusions 235
9. Defending the Practical: The American Response 241
The American Tradition in Science 242
Science and American Technology 243
Science and American Universities 246
The American Physics Community 247
American Silence, 1905 -1907 248
The Contributions of Lewis and Tolman 252
Reaction to Lewis and Tolman 257
The Appeal to Common Sense 259
The Popular Response, 1905-1911 261
Conclusions 263
III. FROM RESPONSE TO ASSIMILATION 265
10. Relativity in America, 1912-1980 267
1911 - 1919: The Lull Before the Storm 271
The Assimilation of Special Relativity Within the Scientific
Community, 1920-1980 273
The Evidence 275
Graduate Textbooks, 1920-1945 277
Advanced Undergraduate Textbooks, 1920-1945 281
Introductory Textbooks, 1920-1945 286
Post World WarlI 287
Bridgman's Operationism and Einstein's Relativity 293
Bridgman's Early Studies of Relativity Theory 296
Being Operational Versus Operationism 297
Spreading Time Through Space, 1959-1961 299
Philosophy and Physics 305
The Popular Response to the Theory of Relativity 307
Conclusions 318
11. Relativity and Revolutions in Science 321
Scientific Revolutions 321
Relativity and Scientific Revolutions 324
IX
Contents
Appendix 1. Trigonometry 327
Appendix 2. Kinematics: The Galilean Description of
Motion 339
Appendix 3. Newtonian Mechanics 365
Appendix 4. The Kinetic Theory of Matter and the
Mechanical World View 417
Appendix 5. Ether Drift Experiments: The Search for the
Absolute Frame of Reference 429
Appendix 6. Some Relativistic Derivations 455
Bibliographic Essay: On Understanding Relativity 477
Index 485
x
Preface
The central subject matter of this book is Einstein's special theory of relativiry.
While it is a book that is written primarily for a lay audience this does not
necessarily mean an audience not versed in the ways of doing science. Rather, this
book is written for anyone wishing to consider the nature of the scientific
enterprise: where ideas come from, how they become established and accepted,
what the relationships are among theories, predictions, and measurements, or the
relationship between ideas in a scientific theory and the values held to be important
within the larger culture.
Some readers will find it strange that I raise any of these issues. It is a common
view in our culture that the status of knowledge within science is totally different
from the status of knowledge in other areas of human endeavor. The word
"science" stems from the Latin word meaning "to know" and indeed, knowledge
which scientists acquire in their work is commonly held to be certain, unyielding,
and absolute. Consider how we use the adjective "scientific." There are investors
and there are scientific investors. There are socialists and there are scientific
socialists. There are exterminators and there are scientific exterminators. We all
know how the modifier "scientific" inttudes in our daily life. It is the purpose of
this book to challenge the belief that scientific knowledge is different from other
kinds of knowledge.
Other readers are no doubt aware that scientific theories that at one time are
generally accepted are later rejected as insufficient or inaccurate. This does not
affect the commitment of many of these readers to the notion that scientific
Xl
