Table of Contents

[PREFACE][iii]
[Table of Contents][xiii]
I. [THE EINSTEIN $5,000 PRIZE][1]
[The Donor and the Prize][2]
[The Judges][5]
[Three Thousand Words][7]
[The Competing Essays][9]
[Looking for the Winner][12]
[The Winner of the Prize][16]
II. [THE WORLD—AND US][19]
[Getting Away from the Greek Ideas][21]
[Relativism and Reality][23]
[Laws of Nature][26]
[Concepts and Realities][29]
[The Concepts of Space and Time][33]
[The Reference Frame for Space][36]
[Time and the Coordinate System][38]
[The Choice of a Coordinate Frame][41]
III. [THE RELATIVITY OF UNIFORM MOTION][46]
[Who Is Moving?][48]
[Mechanical Relativity][50]
[The Search for the Absolute][52]
[The Ether and Absolute Motion][55]
[The Earth and the Ether][57]
[A Journey Upstream and Back][58]
[The Michelson-Morley Experiment][60]
[The Verdict][63]
[The “Contraction” Hypothesis][65]
[Taking the Bull by the Horns][68]
[Questions of Common Sense][71]
[Shifting the Mental Gears][72]
IV. [THE SPECIAL THEORY OF RELATIVITY][76]
[Light and the Ether][78]
[The Measurement of Time and Space][80]
[The Problem of Communication][83]
[An Einsteinian Experiment][86]
[Who Is Right?][89]
[The Relativity of Time and Space][91]
[Relativity and Reality][95]
[Time and Space in a Single Package][98]
[Some Further Consequences][100]
[Assumption and Consequence][104]
[Relativity and the Layman][106]
[Physics vs. Metaphysics][109]
V. [THAT PARALLEL POSTULATE][111]
[Terms We Cannot Define][113]
[Laying the Foundation][115]
[The Rôle of Geometry][119]
[What May We Take for Granted?][122]
[And What Is It All About?][124]
[Euclid’s Geometry][126]
[Axioms Made to Order][128]
[Locating the Discrepancy][130]
[What the Postulate Really Does][132]
[The Geometry of Surfaces][133]
[Euclidean or Non-Euclidean][137]
VI. [THE SPACE-TIME CONTINUUM][141]
[The Four-Dimensional World of Events][144]
[A Continuum of Points][146]
[The Continuum in General][148]
[Euclidean and Non-Euclidean Continua][150]
[Our World of Four Dimensions][155]
[The Curvature of Space-Time][158]
[The Question of Visualization][162]
[What It All Leads To][165]
VII. [RELATIVITY][169]
[The Mechanical Principle of Relativity][170]
[The Special Principle of Relativity][171]
[The Four Dimensional Continuum][173]
[Gravitation and Acceleration][174]
[The General Principle of Relativity][177]
VIII. [THE NEW CONCEPTS OF TIME AND SPACE][181]
[A World of Points][183]
[The Four-Dimensional World of Events][185]
[Successive Steps Toward Generality][187]
[Gravitation and Acceleration][189]
[Einstein’s Time-Space World][191]
[The Layman’s Last Doubt][193]
IX. [THE PRINCIPLE OF RELATIVITY][195]
[The Behavior of Light][197]
[Space and Time][198]
[The World of Reality][201]
[Accelerated Motion][203]
X. [SPACE, TIME AND GRAVITATION][206]
[The External World and its Geometry][208]
[Gravitation and its Place in the Universe][211]
[Gravitation and Space-Time][214]
XI. [THE PRINCIPLE OF GENERAL RELATIVITY][218]
[Gravitation and Acceleration][220]
[Paths Through the World of Four Dimensions][223]
[The Universe of Space-Time][225]
XII. [FORCE VS. GEOMETRY][230]
[The Relativity of Uniform Motion][233]
[Universal Relativity][235]
[The Geometry of Gravitation][237]
XIII. [AN INTRODUCTION TO RELATIVITY][240]
[The Electromagnetic Theory of Light][241]
[The Michelson-Morley Experiment][243]
[The Lorentz Transformation][245]
[The First Theory of Relativity][246]
[The Inclusion of Gravitation][248]
XIV. [NEW CONCEPTS FOR OLD][251]
[The World-Frame][253]
[The World-Fabric][257]
[Einstein’s Results][261]
XV. [THE NEW WORLD][265]
[The World Geometry][267]
[The Genesis of the Theory][270]
[The Time Diagram][273]
XVI. [THE QUEST OF THE ABSOLUTE][276]
[The Gravitational Hypothesis][281]
[The Special Relativity Theory][284]
XVII. [THE PHYSICAL SIDE OF RELATIVITY][287]
XVIII. [THE PRACTICAL SIGNIFICANCE OF RELATIVITY][306]
[The Special Theory and Its Surprising Consequences][309]
[The Generalization][313]
[The Tests][315]
XIX. [EINSTEIN’S THEORY OF RELATIVITY][318]
XX. [EINSTEIN’S THEORY OF GRAVITATION][327]
XXI. [THE EQUIVALENCE HYPOTHESIS][334]
XXII. [THE GENERAL THEORY][338]

I.

THE EINSTEIN $5,000 PRIZE

How the Contest Came to be Held, and Some of the Details of its Conduct

BY THE EDITOR

In January, 1909, an anonymous donor who was interested in the spread of correct scientific ideas offered through the Scientific American a prize of $500 for the best essay explaining, in simple non-technical language, that paradise of mathematicians and bugaboo of plain ordinary folk—the fourth dimension. Many essays were submitted in this competition, and in addition to that of the winner some twenty were adjudged worthy of ultimate publication. It was felt that the competition had added distinctly to the popular understanding of this significant subject; that it had done much to clear up popular misconception of just what the mathematician means when he talks of four or even more dimensions; and that it had therefore been as successful as it was unusual in character.

In November, 1919, the world was startled by the announcement from London that examination of the photographs taken during the total solar eclipse of May 29th had been concluded, and that predictions based upon the Einstein theories of relativity had been verified. In the reaction from the long surfeit of war news an item of this sort was a thoroughly journalistic one. Long cable dispatches were carried in the news columns all over the world; Einstein and his theories were given a prominent place on the front pages day after day; leading scientists in great number were called upon to tell the public through the reportorial medium just what the excitement was all about, just in what way the classical scientific structure had been overthrown.

Instead of being a mere nine days’ wonder, the Einstein theories held their place in the public mind. The more serious periodicals devoted space to them. First and last, a very notable group of scientific men attempted to explain to the general reader the scope and content of Einstein’s system. These efforts, well considered as they were, could be no more than partially successful on account of the very radical character of the revisions which the relativity doctrine demands in our fundamental concepts. Such revisions cannot be made in a day; the average person has not the viewpoint of the mathematician which permits a sudden and complete exchange of one set of fundamentals for another. But the whole subject had caught the popular attention so strongly, that even complete initial failure to discover what it was all about did not discourage the general reader from pursuing the matter with determination to come to some understanding of what had happened to Newton and Newtonian mechanics.