Relativity: The Special and General Theory

‘When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That’s relativity.’ Dealing with the theory of relativity— special relativity and general relativity—and the considerations on the universe as a whole, this book gives an insight into the scientific theory about the relationship between space and time, the theory of gravitation and the universe. A Nobel laureate, Einstein’s research and theories changed the world. First published in 1916, Relativity: The Special and the General Theory is regarded as the most significant work in modern physics. It continues to remain popular and highly influential.

                              CONTENTS

Preface.............................................................................................. 5

Part I. The Special Theory of Relativity............................................ 6

1. Physical Meaning of Geometrical Propositions......................... 7
2. The System of Co-ordinates.................................................... 9
3. Space and Time in Classical Mechanics................................. 12
4. The Galileian System of Co-ordinates.................................... 14
5. The Principle of Relativity in the Restricted Sense.................. 15
6. The Theorem of the Addition of Velocities Employed in
   Classical Mechanics............................................................. 18
7. The Apparent Incompatibility of the Law of Propagation of
   Light with the Principle of Relativity..................................... 19
8. On the Idea of Time in Physics.............................................. 22
9. The Relativity of Simultaneity............................................... 25
10. On the Relativity of the Conception of Distance...................... 27
11. The Lorentz Transformation.................................................. 28
12. The Behaviour of Measuring-Rods and Clocks in Motion........ 32
13. Theorem of the Addition of Velocities. The Experiment
    of Fizeau............................................................................. 35
14. The Heuristic Value of the Theory of Relativity...................... 38
15. General Results of the Theory............................................... 39
16. Experience and the Special Theory of Relativity..................... 43
17. Minkowski’s Four-Dimensional Space................................... 47

Part II. The General Theory of Relativity....................................... 50

1. Special and General Principle of Relativity............................ 51
2. The Gravitational Field........................................................ 54
3. The Equality of Inertial and Gravitational Mass as
   an Argument for the General Postulate of Relativity............... 56

In What Respects Are the Foundations of Classical
Mechanics and of the Special Theory of Relativity Unsatisfactory?... 59

1. A Few Inferences from the General Principle of Relativity..... 61
2. Behaviour of Clocks and Measuring-Rods on a Rotating

Body of Reference................................................................ 64

1. Euclidean and Non-Euclidean Continuum........................... 67
2. Gaussian Co-Ordinates....................................................... 70
3. The Space-Time Continuum of the Special Theory of

Relativity Considered as a Euclidean Continuum.................. 73

1. The Space-Time Continuum of the General Theory of

Relativity is Not a Euclidean Continuum.............................. 75

1. Exact Formulation of the General Principle of Relativity....... 78
2. The Solution of the Problem of Gravitation on the Basis of
   the General Principle of Relativity....................................... 81

Part III. Considerations on the Universe as a Whole........................ 84

1. Cosmological Difficulties of Newton’s Theory........................ 85
2. The Possibility of a “Finite” and yet “Unbounded” Universe... 87
3. The Structure of Space According to the General
   Theory of Relativity............................................................. 91

Appendix I. Simple Derivation of the Lorentz Transformation [Supplementary to Section XI]      93

Appendix II. Minkowski’s Four-Dimensional Space (“World”) [Supplementary to Section XVII] 98

Appendix III. The Experimental Confirmation of the General
Theory of Relativity..................................................... 100

1. 1. Motion of the Perihelion of Mercury....................... 101
   2. Deflection of Light by a Gravitational Field............. 102
   3. Displacement of Spectral Lines Towards the Red...... 104

Appendix IV. The Structure of Space According to the General Theory
of Relativity [Supplementary to Section XXXII].............. 108