PREFACE

A distinguished German authority on mathematical physics, writing recently on the theory of Relativity, declared that if his publishers had been willing to allow him sufficient paper and print he could have explained what he wished to convey without using a single mathematical formula. Such success is conceivable. Mathematical methods present, however, two advantages. Their terminology is precise and concentrated, in a fashion which ordinary language cannot afford to adopt. Further, the symbols which result from their employment have implications which, when brought to light, yield new knowledge. This is deductively reached, but it is none the less new knowledge. With greater precision than is usual, ordinary language may be made to do some, if not a great deal, of this work for which mathematical methods are alone quite appropriate. If ordinary language can do part of it an advantage may be gained. The difficulty that attends mathematical symbolism is the accompanying tendency to take the symbol as exhaustively descriptive of reality. Now it is not so descriptive. It always embodies an abstraction. It accordingly leads to the use of metaphors which are inadequate and generally untrue. It is only qualification by descriptive language of a wider range that can keep this tendency in check. A new school of mathematical physicists, still, however, small in number, is beginning to appreciate this.

But for English and German writers the new task is very difficult. Neither Anglo-Saxon nor Saxon genius lends itself readily in this direction. Nor has the task as yet been taken in hand completely, so far as I am aware, in France. Still, in France there is a spirit and a gift of expression which makes the approach to it easier than either for us or for the Germans. Lucidity in expression is an endowment which the best French writers possess in a higher degree than we do. Some of us have accordingly awaited with deep interest French renderings of the difficult doctrine of Einstein.

M. Nordmann, in addition to being a highly qualified astronomer and mathematical-physicist, possesses the gift of his race. The Latin capacity for eliminating abstractness from the description of facts is everywhere apparent in his writing. Individual facts take the places of general conceptions, of Begriffe. The language is that of the Vorstellung, in a way that would hardly be practicable in German. Nor is our own language equal to that of France in delicacy of distinctive description. This book could hardly have been written by an Englishman. But the difficulty in his way would have been one as much of spirit as of letter. It is the lucidity of the French author, in combination with his own gift of expression, that has made it possible for the translator to succeed so well in overcoming the obstacles to giving the exposition in our own tongue this book contains. The rendering seems to me, after reading the book both in French and in English, admirable.

M. Nordmann has presented Einstein’s principle in words which lift the average reader over many of the difficulties he must encounter in trying to take it in. Remembering Goethe’s maxim that he who would accomplish anything must limit himself, he has not aimed at covering the full field to which Einstein’s teaching is directed. But he succeeds in making many abstruse things intelligible to the layman. Perhaps the most brilliant of his efforts in this direction are Chapters [V] and [VI], in which he explains with extraordinary lucidity the new theory of gravitation and of its relation to inertia. I think that M. Nordmann is perhaps less successful in the courageous attack he makes in his [third chapter] on the obscurity which attends the notion of the “Interval.” But that is because the four-dimensional world, which is the basis of experience of space and time for Einstein and Minkowski, is in itself an obscure conception. Mathematicians talk about it gaily and throw its qualities into equations, despite the essential exclusion from it of the measurement and shape which actual experience always in some form involves. They lapse on that account into unconscious metaphysics of a dubious character. This does not destroy the practical value of their equations, but it does make them very unreliable as guides to the character of reality in the meaning which the plain man attaches to it. Here, accordingly, we find the author of this little treatise to be a good man struggling with adversity. If he could make the topic clear he would. But then no one has made it clear excepting as an abstraction which works, but which, despite suggestions made to the contrary, cannot be clothed for us in images.

This, however, is the fault, not of M. Nordmann himself, but of a phase of the subject. With the subject in its other aspects he deals with the incomparable lucidity of a Frenchman. I know no book better adapted than the one now translated to give the average English reader some understanding of a principle, still in its infancy, but destined, as I believe, to transform opinion in more regions of knowledge than those merely of mathematical physics.

Haldane

CONTENTS

Preface by the Rt. Hon. Viscount Haldane, O.M.[pp.  5-8]
Introduction[pp. 13-15]
CHAPTER I
THE METAMORPHOSES OF
SPACE AND TIME

Removing the mathematical difficulties—The pillars
of knowledge—Absolute time and space, from
Aristotle to Newton—Relative time and space,
from Epicurus to Poincaré and Einstein—
Classical Relativity—Antinomy of stellar
aberration and the Michelson experiment

[pp. 17-31]
CHAPTER II
SCIENCE IN A NO-THOROUGHFARE

Scientific truth and mathematics—The precise function
of Einstein—Michelson’s experiment, the Gordian knot
of science—The hesitations of Poincaré—The strange,
but necessary, Fitzgerald-Lorentz hypothesis—The
contraction of moving bodies—Philosophical and
physical difficulties

[pp. 32-52]
CHAPTER III
EINSTEIN’S SOLUTION

Provisional rejection of ether—Relativist
interpretation of Michelson’s experiment—New aspect
of the speed of light—Explanation of the contraction
of moving bodies—Time and the four dimensions of
space—Einstein’s “Interval” the only material
reality

[pp. 53-72]
CHAPTER IV
EINSTEIN’S MECHANICS

The mechanical foundation of all the sciences—
Ascending the stream of time—The speed of
light an impassable limit—The addition of speeds
and Fizeau’s experiment—Variability of mass—
The ballistics of electrons—Gravitation and light
as atomic microcosms—Matter and energy—
The death of the sun

[pp. 73-100]
CHAPTER V
GENERALISED RELATIVITY

Weight and inertia—Ambiguity of the Newtonian
law—Equivalence of gravitation and accelerated
movement—Jules Verne’s projectile and the principle
of inertia—Why rays of light are subject to
gravitation—How light from the stars is
weighed—An eclipse as a source of light

[pp. 101-123]
CHAPTER VI
THE NEW CONCEPTION
OF GRAVITATION

Geometry and reality—Euclid’s geometry and
others—Contingency of Poincaré’s criterion—
The real universe is not Euclidean but Riemannian—
The avatars of the number π—The point of view of
the drunken man—Straight and geodetic lines—The
new law of universal attraction—Explanation of the
anomaly of the planet Mercury—Einstein’s theory
of gravitation

[pp. 124-147]
CHAPTER VII
IS THE UNIVERSE INFINITE?

Kant and the number of the stars—Extinct stars and
dark nebulæ—Extent and aspect of the astronomical
universe—Different kinds of universes—Poincaré’s
calculation—Physical definition of the infinite—
The infinite and the unlimited—Stability and
curvature of cosmic space-time—Real and virtual
stars—Diameter of the Einsteinian universe—
The hypothesis of globes of ether

[pp. 148-159]
CHAPTER VIII
SCIENCE AND REALITY

The Einsteinian absolute—Revelation by science—
Discussion of the experimental bases of Relativity—
Other possible explanations—Arguments in favour
of Lorentz’s real contraction—Newtonian space
may be distinct from absolute space—The real is
a privileged form of the possible—Two attitudes
in face of the unknown

[pp. 160-172]
CHAPTER IX
EINSTEIN OR NEWTON?

Recent discussion of Relativism at the Academy
of Sciences—Traces of the privileged space
of Newton—The principle of causality,
the basis of science—Examination of M.
Painlevé’s objections—Newtonian arguments
and Relativist replies—M. Painlevé’s formulas
of gravitation—Fecundity of Einstein’s theory—
Two conceptions of the world—Conclusion

[pp. 173-185]

INTRODUCTION