Read The Faber Book of Science Online
Authors: John Carey
Albert Einstein (1879–1955) became a cultural icon in his own lifetime. While still a young man he provided physicists with entirely new ways of thinking about space, time and gravitation. In later years his appearance and personality – the thistledown hair-do, the sad chimpanzee face, the pacifism, the simple tastes – gave the west its paramount symbol of benevolent scientific genius.
Born in Ulm, Germany, Einstein went to school in Munich, where his father ran a small engineering works. The pedantic educational regime daunted him, and he was credited with little academic ability. Two of his uncles encouraged his interest in physics and maths, though, and he studied these subjects as an undergraduate at Zurich Polytechnic. Becoming a Swiss citizen, he taught maths, and acted as an examiner at the Swiss Patent Office in Berne. In 1905, at the age of 26, he published four epoch-making scientific papers, including his Special Theory of Relativity. The General Theory followed in 1916.
In his
Popular
Exposition
of the two theories (1920), Einstein explains for non-scientific readers how his ideas differ from those of orthodox physics. In orthodox physics the distance between two points on a rigid body is assumed to be always the same, irrespective of whether the body is in motion. Measurement of the time interval between two events is also assumed to be unaffected by motion. These assumptions accord with the dictates of Newton, who had proclaimed (in
Mathematical
Principles,
1686)
that space and time were ‘absolute’:
Absolute Space, in its own nature, without regard to anything external, remains always similar and immovable … Absolute, True and Mathematical Time, of itself, and from its own nature, flows equably without regard to anything external.
To illustrate how his own theory differs from these classic views, Einstein asks us to imagine a train speeding along an embankment. He also asks us to imagine two observers: one a passenger on the train, the other a man standing on the embankment watching the train go by. In orthodox physics the train would, of course, be the same length to both observers. But in Einstein’s theory it is not. To the watcher on the embankment, it is shorter. This
shortening is not due to optical illusion, but to a change in the nature of space itself, caused by motion.
The same principle holds whatever moving body we substitute for the train. Suppose that the passenger is holding a metre rod, and pointing it in the direction of the train’s motion, then the length of the rod seen by the watcher on the embankment will, Einstein asserts, be less than a metre, by a mathematically calculable fraction:
The rigid rod is shorter when in motion than when at rest, and the more quickly it is moving the shorter is the rod.
The rod will shrink only in the direction of its motion. Its length will diminish, but its thickness will remain identical to what it was at rest.
As with space, so with time. Einstein asks us to imagine a clock on the train. The time that elapses between two successive ticks, when it is stationary, is exactly one second, and to the passenger on the train, seated by the clock, the interval will still be one second when the train is moving. But to the watcher on the embankment the interval, Einstein states, will be greater:
As a consequence of its motion the clock goes more slowly than when at rest.
The same will apply whatever measured interval we substitute for clock ticks. Heartbeats, for example, or biological growth, or the process of human ageing, will all be slower as observed from the embankment.
These effects of foreshortening and slowing down are all reciprocal. That is, if the passenger on the train looked out at the watcher on the embankment, and if the watcher had a metre rod, which he held parallel to the rails, and a clock identical with the passenger’s, then the watcher’s metre rod would be shorter than the passenger’s and the watcher’s clock would go slower. This reciprocity follows from the fact that in Einstein’s theory the watcher on the embankment is no less in motion than the passenger:
Every motion must only be considered as a relative motion. Returning to the illustration we have frequently used of the embankment and the railway carriage, we can express the fact of motion here taking place in the following two forms, both of which are equally justifiable:
(a) The carriage is in motion relative to the embankment.
(b) The embankment is in motion relative to the carriage.
Einstein emphasizes that the effects he describes become discernible only at very high speeds, approaching the speed of light:
We have experience of such rapid motions only in the case of electrons and ions; for other motions the variation from the laws of classical mechanics are too small to make themselves evident in practice.
Nevertheless the many popular accounts of Relativity Theory published in the 1920s continued to draw their illustrations from everyday life, so as to give the public graphic means of imagining the new concepts. Bertrand Russell’s
The
ABC
of
Relativity
(1926) retained Einstein’s railway train but, in keeping with the ethos of an upper-middle-class pastoral England, gave it a dining car and made the watcher on the embankment a fisherman:
Let us suppose that you are in a train on a long straight railway, and that you are travelling at three-fifths of the velocity of light. Suppose that you measure the length of your train, and find that it is a hundred yards. Suppose that the people who catch a glimpse of you as you pass succeed by skilful scientific methods, in taking observations which enable them to calculate the length of your train. If they do their work correctly, they will find that it is eighty yards long. Everything in the train will seem to them shorter in the direction of the train than it does to you. Dinner plates, which you see as ordinary circular plates, will look to the outsider as if they were oval: they will seem only four-fifths as broad in the direction in which the train is moving as in the direction of the breadth of the train. And all this is reciprocal. Suppose you see out of the window a man carrying a fishing-rod which by his measurement, is fifteen feet long. If he is holding it upright, you will see it as he does; so you will if he is holding it horizontally at right angles to the railway. But if he is pointing it along the railway, it will seem to you to be only twelve feet long. All lengths in the direction of motion are diminished by twenty per cent, both for those who look into the train from outside and for those who look out of the train from inside.
The astronomer A. S. Eddington in his
Space,
Time
and
Gravitation
(1920) substituted for Einstein’s locomotive an advanced type of aircraft with an airman lying full length on the floor.
Suppose that by development in the powers of aviation, a man flies past us at the rate of 161,000 miles a second. We shall suppose that he
is in a comfortable travelling conveyance in which he can move about, and act normally, and that his length is in the direction of the flight. If we could catch an instantaneous glimpse as he passed, we should see a figure about three feet high, but with the breadth and girth of a normal human being. And the strange thing is that he would be sublimely unconscious of his own undignified appearance. If he looks in a mirror in his conveyance, he sees his usual proportions … But when he looks down on us, he sees a strange race of men who have apparently gone through some flattening-out process: one man looks hardly ten inches across the shoulders; another standing at right angles is almost ‘length and breadth without thickness’. As they turn about they change appearance like the figures seen in the old-fashioned convex mirrors. If the reader has watched a cricket match through a pair of prismatic binoculars, he will have seen this effect exactly.
It is the reciprocity of these appearances – that each party should think the other has contracted – that is so difficult to realize. Here is a paradox beyond even the imagination of Dean Swift. Gulliver regarded the Lilliputians as a race of dwarfs; and the Lilliputians regarded Gulliver as a giant. That is natural. If the Lilliputians had appeared dwarfs to Gulliver, and Gulliver had appeared a dwarf to the Lilliputians – but no! that is too absurd for fiction, and is an idea only to be found in the sober pages of science.
It is not only in space, but in time that these strange variations occur. If we observed the aviator carefully we should infer that he was unusually slow in his movements; and events in the conveyance moving with him would be similarly retarded – as though time had forgotten to go on. His cigar lasts twice as long as ours.
But here again reciprocity comes in, because in the aviator’s opinion it is we who are travelling at 161,000 miles a second past him; and when he has made all allowances, he finds that it is we who are sluggish. Our cigar lasts twice as long as his.
Whereas in Newtonian physics space and time were absolute, in Einstein’s theory, as these examples illustrate, they become fluid. Space is involved in time, and time in space. For Einstein space and time cease to exist as separate concepts. All events occur in a new (and unimaginable) ‘continuum’ called space-time. Unlike the old geometry, the geometry of this continuum does not contain any straight lines, but is curved. Left to themselves, objects move in curves within it. But large masses, such as the sun, cause ‘puckers’ in
space-time
,
affecting the motion of any object near them. According to Einstein, gravity is the result of these puckers, rather than (as Newton had believed) of a force operating between masses.
Working on this assumption Einstein predicted that the light from a distant star would be ‘bent’ by the sun’s gravitational field as it passed close to the sun.
The occurrence of a solar eclipse in 1919 gave scientists a chance of testing this prediction (it is only during a solar eclipse that stars near the sun can be observed), and accordingly two British expeditions were sent to photograph the eclipse, one, under Eddington, to the Isle of Principe in West Africa, the other to Brazil. They reported that the apparent displacement of stars near the sun was as Einstein had predicted.
When this news broke in November 1919 it projected relativity theory into the world’s headlines. ‘Light All Askew In The Heavens: Einstein’s Theory Triumphs’, announced the
New
York
Times.
The London
Times
carried an article headed ‘The Fabric Of The Universe’ hailing Einstein’s theory as ‘a new philosophy that will sweep away nearly all that has been hitherto accepted as the axiomatic basis of physical thought’. The effects of the new theory on time and space also inspired the cartoonists and limerick-writers, like Arthur Buller:
There was a young lady named Bright,
Who travelled much faster than light.
She started one day
In the relative way
And returned on the previous night.
The
Scientific
American
ran a competition for the clearest 3,000-word account of Einstein’s theory. Several world-famous scientists entered, but the prize ($5,000) went to Lyndon Bolton, an Irish-born schoolmaster working in the London Patent Office (appropriately, since Einstein had been a
schoolmaster
working in the Swiss Patent Office when he formulated the theory).
Having explained the Special Theory (much as Russell and Eddington do above) Bolton’s prize-winning essay (printed in the
Scientific
American,
5 February 1921) goes on to tackle the more difficult General Theory which, unlike the Special Theory, takes account of gravitational fields. Developing an illustration used by Einstein himself, Bolton asks us to imagine a simulated gravitational field, consisting of a large revolving disk with a man standing on it. Since the disk is isolated in space, the man is not aware it is revolving (any more than we are aware the earth is). This is (as Bolton concedes) not a perfect model of a gravitational field, because the man will feel himself thrown away from the centre by centrifugal force, whereas in a gravitational field he would feel himself pulled towards the centre. However, in other respects it is, Bolton
shows, a useful model for understanding what happens to conventional geometry when it is put into a gravitational field:
Let us note the experiences of an observer on a rotating disk which is isolated so that the observer has no direct means of perceiving the rotation …
He will notice as he walks about on the disk that he himself and all the objects on it, whatever their constitution or state, are acted upon by a force directed away from a certain point upon it and increasing with the distance from that point. This point is actually the center of rotation, though the observer does not recognize it as such. The space on the disk in fact presents the characteristic properties of a gravitational field. The force differs from gravity as we know it by the fact that it is directed away from instead of toward a center, and it obeys a different law of distance, but this does not affect the characteristic properties that it acts on all bodies alike, and cannot be screened from one body by the interposition of another. An observer aware of the rotation of the disk would say that the force was centrifugal force; that is, the force due to inertia which a body always exerts when it is accelerated.
Next suppose the observer to stand at the point of the disk where he feels no force, and to watch someone else comparing, by repeated applications of a small measuring rod, the circumference of a circle having its center at that point, with its diameter. The measuring rod when laid along the circumference is moving lengthwise relatively to the observer, and is therefore subject to contraction by his reckoning. When laid radially to measure the diameter this contraction does not occur. The rod will therefore require a greater proportional number of applications to the circumference than to the diameter, and the number representing the ratio of the circumference of the circle to the diameter thus measured will therefore be greater than 3.14159+, which is its normal value. Moreover the relative velocity decreases as the center is approached, so that the contraction of the measuring rod is less when applied to a smaller circle; and the ratio of the circumference to the diameter, while still greater than the normal, will be nearer to it than before, and the smaller the circle the less the difference from the normal. For circles whose centers are not at the point of zero force the confusion is still greater, since the velocities relative to the observer of points on them now change from point to point. The whole scheme of
geometry as we know it is thus disorganized. Rigidity becomes an unmeaning term since the standards by which alone rigidity can be tested are themselves subject to alteration …