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### Einstein's Theory of Relativity

**Einstein's Theory of Relativity
94 Pages
B.A. Westwood**

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Preface:

Even after over ninety years, Einstein's theory of Relativity still has the reputation of being difficult to understand. If this is true it is not because of mathematical difficulties - this book rarely uses anything more complicated than a square root sign - but because Relativity involves us in thinking very hard about the making and interpretation of measurements in physics. This makes it all the more useful for students of physics to study Relativity, even though, unless they work in a few special fields, they are unlikely ever to observe relativistic effects in practice.

TOC

Introduction ix

Chapter 1

1. The Michelson-Morley experiment 1

1.1 Electromagnetic waves and the ether 1

1 .2 The velocity of the earth through the ether 2

1.3 The Michelson-Morley experiment 3

1 .4 Explanations of the null result 6

Additional exercises 7

Chapter 2

2. Einstein's postulates 8

2.1 Coordinate systems 8

2.2 Inertial systems 9

2.3 Einstein's two postulates 11

2.4 The Relativity postulate 11

2.5 The postulate of the constant velocity of light 12

Additional exercises 13

Chapter 3

3. The Lorentz transformation 14

3.1 Time dilation 14

3.2 An experimental test of time dilation 15

3.3 Relativity and simultaneity 16

3.4 The problem of synchronizing clocks 17

3.5 Length contraction 19

3.6 Perpendicular lengths 20

3.7 Derivation of the Lorentz transformation 21

3.8 Properties of the Lorentz transformation 23

3.9 The symmetry between coordinate systems 24

3.10 The Twin Paradox 25

Additional exercises 26

Chapter 4

4. Velocities and accelerations 28

4. 1 Transformation of velocities in one dimension 28

4.2 The exploding space-ship 29

4.3 The general transformation of velocities 30

4.4 The transformation of angles 31

4.5 The Doppler effect 32

4.6 A resolution of the Twin Paradox 35

4.7 Accelerated motion 37

Additional exercises 38

Chapter 5

5. Relativistic mechanics I 40

5.1 The inadequacy of Newton's Laws 40

5.2 The definition of momentum 42

5.3 Relativistic mass and rest mass 42

5.4 Transformation of momentum and relativistic mass 43

5.5 The invariant form of the transformation laws

5.6 Total energy and E = mc^{2}

5.7 The equivalence of mass and energy

5.8 Summary

Additional exercises

Chapter 6

6. Relativistic mechanics II

6.1 Examples of the use of conservation laws

6.2 Particles with zero rest mass

6.3 Invariant masses

6.4 Forces

Additional exercises

Chapter 7

7. Experimental tests and consequences of Special Relativity 59

7.1 The variation of relativistic mass with velocity 60

7.2 Particle accelerators 61

7.3 Particles, time dilation, and the second postulate 63

7.4 Units of mass, energy, and momentum 64

7.5 Experiments on the equivalence of mass and energy 65

7.6 Particle and anti-particle production 66

Additional exercises 68

Chapter 8

8. General Relativity

8.1 The Principle of Equivalence

8.2 Space and General Relativity

8.3 The gravitational red shift

8.4 Time measurements in General Relativity

8.5 Another solution of the Twin Paradox

Additional exercises

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