Ask a dozen people to name a genius and the odds are that 'Einstein' will spring to their lips. Ask them the meaning of 'relativity' and few of them
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1 Ask a dozen people to name a genius and the odds are that 'Einstein' will spring to their lips. Ask them the meaning of 'relativity' and few of them will be able to tell you what it is. The ABC of Relativity is Bertrand Russell's most brilliant work of scientific popularisation. With marvellous lucidity he steers the reader who has no knowledge of maths or physics through the subtleties of Einstein's thinking; in easily assimilable steps he explains the theories of special and general relativity and describes their practical application (among much else to discoveries about gravitation and the invention of the hydrogen bomb). 'Einstein', wrote Russell, 'revolutionised our conception of the physical world, but the innumerable popular accounts of his theory generally cease to be intelligible at the point where they begin to say something important.' The basic principles of relativity have not changed since Russell first published his lucid guide for the general reader. This new edition takes account of the extension of our knowledge about the theory and its applications.
2 BERTRAND RUSSELL ABC OF RELATIVITY Fourth Revised Edition Edited by Felix Pirani LONDON
3 Preface to the Fourth Edition
4 Contents
5 Chapter 1 Touch and Sight: The Earth and the Heavens Everybody knows that Einstein did something astonishing, but very few people know exactly what it was. It is generally recognised that he revolutionised our conception of the physical world, but the new conceptions are wrapped up in mathematical technicalities. It is true that there are
6 10 ABC of Relativity
7 Touch and Sight 11
8 12 ABC of Relativity
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10 14 ABC of Relativity
11 Touch and Sight 15 exerting themselves, and evidently putting out 'force' in the same way as human beings do. Everybody knew from experience what it is to push or pull, or to be pushed or
12 16 ABC of Relativity their relative position, we cannot say that one is moving while the other is at rest, since the occurrence is merely a change
13 Chapter 2 What Happens and What is Observed A certain type of superior person is fond of asserting that 'everything is relative'. This is, of course, nonsense, because,
14 18 ABC of Relativity perception of a given occurrence differs from another's. Some of these differences are due to differences in the brains or
15 What Happens and What is Observed 19
16 20 ABC of Relativity (about 186,000 miles). It travels from the sun to the earth in about eight minutes, and from the stars in anything from four years to several thousand million. Of course, we cannot
17 What Happens and What is Observed 21 - as subjective, while allowing 'primary' qualities - shapes and positions and sizes - to be genuine properties of physical objects. The physicist's rules were such as would follow from this doctrine. Colours and noises were allowed to be subjective, but due to waves proceeding with a definite velocity - that of light or sound as the case may be - from their source to the eye or ear of the percipient. Apparent shapes vary according to the laws of perspective, but these
18 22 ABC of Relativity
19 What Happens and What is Observed 23
20 24 ABC of Relativity in physics. Since all motion is relative, you may take any body
21 What Happens and What is Observed 25 temporal properties of physical occurrences are found to be
22 Chapter 3
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24 28 ABC of Relativity
25 The Velocity of Light 29
26 30 ABC of Relativity
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28 32 ABC of Relativity at the same spot at the same moment, it also would find that it remained at the centre of the ripples, even if it separated itself widely from the first fly. This is exactly analogous to
29 The Velocity of Light 33 may judge that the time was more or less than an hour. You cannot say that one is right and the other wrong, any more than you could if one used a clock showing Greenwich time
30 34 ABC of Relativity
31 Chapter 4
32 36 ABC of Relativity
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34 38 ABC of Relativity two events are simultaneous according to the definition, there
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36 40 ABC of Relativity
37 Clocks and Foot-rules 41 in Edinburgh, there are four hundred miles and ten hours. We have already seen that other observers will judge the time differently; it is even more obvious that they will judge the
38 42 ABC of Relativity say that the interval 1 between the two events is 'space-like';
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40 44 ABC of Relativity Although AB and AC are different for different observers,
41 Chapter 5 Space-Time
42 46 ABC of Relativity number of such ways of fixing the position in space, all
43 Space-Time 47 we cannot, as before, divide off one of the four as quite independent of the other three. It is not quite true to say that there is no longer any distinction between time and space. As we have seen, there are time-like intervals and space-like intervals. But the distinction is of a different sort from that which was formerly assumed. There is no longer a universal time which can be
44 48 ABC of Relativity fundamental, but is at any rate a help in understanding the state of affairs we have been describing. He maintained that
45 Space-Time 49
46 50 ABC of Relativity
47 Space-Time 51 get different results from their measurements. Thus the trouble about time is at the bottom of the trouble about distance.
48 52 ABC of Relativity of the state of the world at a given instant is, for another
49 Chapter 6 The Special Theory of Relativity
50 54 ABC of Relativity other scientific hypothesis not capable of direct verification. But a new set of facts began to be discovered, and gradually the whole picture was changed.
51
52 56 ABC of Relativity of his results must almost be ascribed to intuition. Now these
53 The Special Theory of Relativity 57
54 58 ABC of Relativity
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56 60 ABC of Relativity But when, instead of comparing events at the same place on the earth, we compare events at widely separated places, the results are still more odd. Let us now take all the events
57 The Special Theory of Relativity 61 travellers. We must first take five-fourths of the time as estimated by the earth-dwellers, and then subtract three-
58 62 ABC of Relativity
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60 64 ABC of Relativity Y such that OY is equal to OX (X is the point of the railway where the lightning strikes). Draw YM perpendicular to the
61 The Special Theory of Relativity 65
62 Chapter 7
63 Intervals in Space-Time 67 the restriction, Einstein was led to his new law of gravitation, which we shall consider presently. The work was extraordinarily difficult, and occupied him for ten years. The
64 68 ABC of Relativity though few physicists in modern times have believed in
65 Intervals in Space-Time 69
66 70 ABC of Relativity The next step of importance is due to Descartes, who
67 Intervals in Space-Time 71
68 72 ABC of Relativity convince yourself of this by experiment. If not, you can easily
69 Intervals in Space-Time 73 angles of the triangle add up to two right angles: they will
70 74 ABC of Relativity
71 Intervals in Space-Time 75
72 76 ABC of Relativity between two points would be given by a formula analogous
73 Intervals in Space-Time 77
74 Chapter 8 Einstein's Law of Gravitation Before tackling Einstein's law, it is as well to convince ourselves, on logical grounds, that Newton's law of gravitation cannot be quite right. Newton said that between any two particles of matter there
75 Einstein's Law of Gravitation 79
76 80 ABC of Relativity
77 Einstein's Law of Gravitation 81
78 82 ABC of Relativity
79 Einstein's Law of Gravitation 83
80 84 ABC of Relativity physical phenomena. We know certain things. We know that the old Newtonian physics is very nearly accurate when our
81 Einstein's Law of Gravitation 85 that there should be no gravitation in the region; it is enough if the intensity of gravitation is practically the same
82 86 ABC of Relativity move, we are confined to time-like intervals. The interval
83 Einstein's Law of Gravitation 87
84 88 ABC of Relativity
85 Einstein's Law of Gravitation 89 myself. The most interesting point about it is that it makes the law no longer the result of action at a distance; the sun
86 90 ABC of Relativity
87 Chapter 9 Proofs of Einstein's Law of Gravitation The reasons for accepting Einstein's law of gravitation rather
88 92 ABC of Relativity perturbations caused by the other planets, but this small
89 Proofs of Einstein's Law of Gravitation 93
90 94 ABC of Relativity you hear is only due to the fact that the train was first approaching and then receding. To people in the train, there was no change of note. This is not the effect about which the prediction was made. According to the new theory,
91 Proofs of Einstein's Law of Gravitation 95 predicted effect has now been accurately confirmed by many different experiments. There are many other differences between the new law of
92 96 ABC of Relativity
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94 98 ABC of Relativity Thus if we mean 'gravitational mass' in sense (1), that is to say, the way a body responds to gravitation, we find that 'the equality of inertial and gravitational mass', which sounds
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96 Chapter 10 Mass, Momentum, Energy, and Action The pursuit of quantitative precision is as arduous as it is
97 Mass, Momentum, Energy, and Action 101
98 102 ABC of Relativity 'weights' are altered just as much as the body to be weighed,
99 Mass, Momentum, Energy, and Action 103
100 104 ABC of Relativity
101 Mass,
102 106 ABC of Relativity how this comes about is not easy: nevertheless we will make the attempt. In popular talk, 'mass' and 'energy' do not mean at all the same thing. We associate 'mass' with the idea of a fat person
103 Mass, Momentum, Energy,
104 108 ABC of Relativity
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106 110 ABC of Relativity while its kinetic energy, according to the usual formula, will be
107 Mass, Momentum, Energy, and Action 111 important in relativity physics, as well as in the quantum theory. (The quantum is a small amount of action.) The word 'action'
108 112 ABC of Relativity complete with hills and valleys. Such principles, which play
109 Chapter 11 The Expanding Universe We have been dealing hitherto with experiments and observations most of which concern the earth or the solar
110 114 ABC of Relativity galactic scale, is difficult to estimate, and may be revised in the future. (On the galactic scale, distances are often measured in light-years. A light-year is the distance which light travels in a year: you may calculate it by multiplying the speed of light, which is given on p. 20, by the number of seconds in a year, which is 31,536,000. If you convert the answer into miles, it is nearly six million million miles.) The Milky Way, a bright band of stars across the sky which is easily visible on a clear night, is just our edge-on view of
111 The Expanding Universe 115
112 116 ABC of Relativity
113 The Expanding Universe 117
114 118 ABC of Relativity
115 The Expanding Universe 119
116 120 ABC of Relativity
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118 122 ABC of Relativity
119 The Expanding Universe 123 on the resolving of some serious mathematical difficulties; which of the available models is to be preferred at any particular time must depend on the astronomical data.
120 Chapter 12 Conventions and
121 Conventions and Natural Laws 125
122 126 ABC of Relativity
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124 128 ABC of Relativity mathematical expression in question. As a proposition of
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126 130 ABC of Relativity
127 Conventions and Natural Laws 131 Geography, in this sense, includes everything that, as a matter of crude fact, distinguishes one part of space-time from
128 132 ABC of Relativity
129 Chapter 13 The Abolition of 'Force' In the Newtonian system, bodies under the action of no forces
130 134 ABC of Relativity
131 The Abolition of 'Force' 135 mistake. If you insist on adhering to the Euclidean formula
132 136 ABC of Relativity
133 The Abolition of 'Force' 137 There is, of course, some truth in this; the point is to discover exactly what truth. In the first place, images are not 'imaginary'.
134 138 ABC of Relativity
135 The Abolition of 'Force' 139 us to regard the heavenly bodies, although we can only see and not touch them, as more 'real' than an image in a lookingglass. We can now begin to interpret the common-sense notion
136 140 ABC of Relativity
137 Chapter 14 What is Matter?
138 142 ABC of Relativity respectable when it was found to play the same part in electromagnetic phenomena as in the propagation of light.
139 What is Matter? 143
140 144 ABC of Relativity of the disturbance. It will also count as one event in the biography of the particle of matter which is supposed to occupy the centre of the disturbance. Now we find not only that one light-wave travels outward from a centre according to a certain law, but also that, in
141 What is Matter? 145 theory of relativity to clear away so much useless lumber. Common sense imagines that when it sees a table it sees
142 146 ABC of Relativity What I wish to suggest may be put as follows. Everything that occurs elsewhere, owing to the existence of an atom, can
143 What is Matter? 147
144 Chapter 15 Philosophical Consequences
145 Philosophical Consequences 149
146 150 ABC of Relativity noticeable; the helium atom weighs measurably less than four separate hydrogen atoms.
147 Philosophical Consequences 151 power of proving facts grow less and less. Logic used to be
148 152 ABC of Relativity
149 Philosophical Consequences 153
150 154 ABC of Relativity
151
Einstein s Theory of Special Relativity Made Relatively Simple!
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