PART II THE GENERAL THEORY OF RELATIVITY
XVIII. Special and General Principle of Relativity . 5 XIX. The Gravitational Field . . . .6 XX. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity ..... XXI. In what Respects are the Foundations of Classical Mechanics and of the Special Theory of Relativity unsatisfactory? . XXII. A Few Inferences from the General Principle of Relativity ..... XXIII. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference . XXIV. Euclidean and Non-Euclidean Continuum XXV. Gaussian Co-ordinates .... XXVI. The Space-time Continuum of the Special Theory of Relativity considered as a Euclidean Continuum
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XXVII. The Space-time Continuum of the General Theory of Relativity is not a Euclidean Continuum . . . . 93 XXVIII. Exact Formulation of the General Principle of Relativity . . . . 97 XXIX. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity ..... 100
PART III
CONSIDERATIONS ON THE UNIVERSE AS A WHOLE
XXX. Cosmological Difficulties of Newton's Theory 105 XXXI. The Possibility of a "Finite" and yet "Unbounded" Universe. . . . 108 XXXII. The Structure of Space according to the General Theory of Relativity . . 113
APPENDICES
I. Simple Derivation of the Lorentz Transformation . 115 II. Minkowski's Four-dimensional Space ("World") [Supplementary to Section XVII.] . . 121 III. The Experimental Confirmation of the General Theory of Relativity . . . .123 (a) Motion of the Perihelion of Mercury . 124 (b) Deflection of Light by a Gravitational Field 126 (c) Displacement of Spectral Lines towards the Red . . . . . 129
BIBLIOGRAPHY . . . . . . 133
RELATIVITY THE SPECIAL AND THE GENERAL THEORY
IThe Special Theory of RelativitySpecial Theory of Relativity
[Geometrical Propositions] IPhysical Meaning of Geometrical Propositions
In your schooldays most of you who read this
book made acquaintance with the noble building of Euclid's geometry, and you remember–-perhaps with more respect than love–-the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. By reason of your past experience, you would certainly regard everyone with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud certainty would leave you immediately if some one were to ask you: "What, then, do you mean by the assertion that these propositions are true?" Let us proceed to give this question a little consideration.