Report on the Relativity Theory of Gravitation - The Physical Society of London Book

THE PHYSICAL SOCIETY LONDON. REPORT OK THE RELATIVITY THEOEY OF GRAVITATION. A. S. EDDINOTON, M. A., M. Sc., F. E. S. M Plumtan Professor of Astronomy and Experimental Philosophy, Cambridge. Price to Non-Fellows, 6 8. net, post free 6s. 3d, Bound in doth, 8s. 6d., post ree 8s 9d LONDON. FLEET WAY PRESS, LTX , 1, 2 AND 3, SALISBURY COUBT, FLEET STBEET 1920. CONTENTS. CHAPTEE L PAGE THE KESTRICTED PRINCIPLE or EELATIVITY 1 1-3. The Michelson-Morley experiment and its significance. 4. The transformation of co-ordinates for a moving observer. 5. Reciprocity of the transformation. 6. Standpoint ot the Principle of Relativity. 7, Transformation of velocity, of den sity and of mass. 8. Scope of the Principle. CHAPTER II. THE KELATIONS OF SPACE, TIME, AND FORCE 14 9-10. Minkowskis transformation. 11. Invanance of 8. 12. Irrelevance of co-ordinate systems to the phenomena, 13-14. The Principle of Equivalence. 15-16. Definition of a field of force by g v . 17. Purpose of the theory of tensors. 18, Nature of space and time in the gravitational field. CHAPTEE III. THE THEORY OF TENSORS 30 19. Notation , definition and elementary properties of tensors. 20. The fundamental tensors associated tensors. 21. Auxili ary formula for the second derivatives of the co-ordinates. 22. Covariant differentiation. 23-24. The Riemann-Ghristoffel ten sor. 26. Summary. CHAPTEE IV. EINSTEINS LAW OF GRAVITATION 41 26. The contracted Eiemann-Christoffel tensor. 27. Limitation of the Principle of Equivalence. 28. The gravitational field of a Dartiole IV. CONTENTS. CHAPTER V. PAGB THE CRUCIAL PHENOMENA 48 29-30. The Equations of Motion. 31. Motion of the Perihelion of Mercury. 32-33. Deflection of a ray of hght 34. Displace ment of spectra lines. CHAPTER VL THE GRAVITATION OF A CONTINUOUS DISTRIBUTION OF MATTER 59 35-36 Equations for a continuous medium. 37 The energy tensor T v , and the equations of hydrodynamics. 38. The Law of Conservation 39. Reaction of the gravitational field on matter. 40. Propagation of gravitation CHAPTER VII. THE PRINCIPLE OF LEAST ACTION 71 41. Expression ot the law of gravitation in the torm ot Lagranges Equations 42. Principle of Least Action. 43. Energy of the gravitational field 44 Method of Hilbert and Lorentz. 45-46. Electromagnetic equations. 47 The JEJther. 48. Summary of the last two chapters CHAPTER VIII. THE CURVATURE OF SPACE AND TIME 82 49. Absolute rotation and the limits ol generalised relativity. 50 Einsteins curved space 51. T e Sitters curved space-time. 52. Boundary Conditions. 53. Conclusion PREFACE TO FIRST EDITION. THE relativity theory of gravitation in its complete form was published by Einstein in November 1915. Whether the theory ultimately proves to be correct or not, it claims attention as one of the most beautiful examples of the power of general mathematical reasoning. The nearest parallel to it is found in the applications of the second law of thermo-dynamics, in which remarkable conclusions are deduced from a single principle without any inquiry into the mechanism of the phenomena similarly, if the principle of equivalence is accepted, it is possible to stride over the difficulties due to ignorance of the nature of gravita tion and arrive directly at physical results. Einsteins theory has been successful in explaining the celebrated astronomical discordance of the motion of the perihelion of Mercury, without introducing any arbitrary constant there is no trace of forced agreement about this prediction. It further leads to interesting conclusions with regard to the deflection of light by a gravitational field, and the displacement of spectral lines on the sun, which may be tested by experiment. The arrangement of this Report is guided by the object of reaching the theory of these crucial phenomena as directly as possible. To make the treatment rather more elementarv, use of the principle of least action and Hamiltonian methods has been avoided and the brief account of these m Chapter VII...Read More