Space, Time and Gravitation - An Outline of the General Relativity Theory

By Arthur Eddington

Written by the English astrophysicist, Sir Arthur Eddington (1882-1944), and originally published in 1920, ‘Space, Time and Gravitation’ outlines the general theory of relativity in astrophysics. This fascinating early work navigates Einstein’s theory through a series of perspectives – that of the experimental physicist, pure mathematician, and relativist, making it a wonderful read for the student, teacher or astrophysics enthusiast today. Contents include: Arthur Eddington; Preface; Prologue; ‘What Is Geometry?’; 1 - The Fitzgerald Contraction; 2 – Relativity; 3 - The World of Four Dimensions; 4 - Fields of force; 5 - Kinds of Space; 6 - The New Law of Gravitation and the Old Law; 7 - Weighing Light; 8 - Other Tests of the Theory; 9 - Momentum and Energy; 10 - towards infinity; 11 - Electricity and Gravitation; 12 - On The Nature of Things; Appendix; Mathematical Notes; Historical Note. This classic text is being republished in a modern and affordable edition, complete with reproductions of the original illustrations and a specially written concise biography.

• Language: English
• Publisher: Read Books Ltd.
• Release date: Mar 6, 2013
• ISBN: 9781447489481

Book preview

RUSSELL.

CHAPTER I

THE FITZGERALD CONTRACTION

In order to reach the Truth, it is necessary, once in one’s life, to put every thing in doubt—so far as possible.

DESCARTES.

WILL it take longer to swim to a point 100 yards up-stream and back, or to a point 100 yards across-stream and back?

In the first case there is a long toil up against the current, and then a quick return helped by the current, which is all too short to compensate. In the second case the current also hinders, because part of the effort is devoted to overcoming the drift down-stream. But no swimmer will hesitate to say that the hindrance is the greater in the first case.

Let us take a numerical example. Suppose the swimmer’s speed is 50 yards a minute in still water, and the current is 30 yards a minute. Thus the speed against the current is 20, and with the current 80 yards a minute. The up journey then takes 5 minutes and the down journey 1 1/4 minutes. Total time, 6 1/4 minutes.

Going across-stream the swimmer must aim at a point E above the point B where he wishes to arrive, so that OE represents his distance travelled in still water, and EB the amount he has drifted down. These must be in the ratio 50 to 30, and we then know from the right-angled triangle OBE that OB will correspond to 40. Since OB is 100 yards, OE is 125 yards, and the time taken is 2 1/2 minutes. Another 2 1/2 minutes will be needed for the return journey. Total time, 5 minutes.

FIG. 1.

In still water the time would have been 4 minutes.

The up-and-down swim is thus longer than the transverse swim in the ratio 6 1/4 : 5 minutes. Or we may write the ratio

which shows how the result depends on the ratio of the speed of the current to the speed of the swimmer, viz. 30/50.

A very famous experiment on these lines was tried in America in the year 1887. The swimmer was a wave of light, which we know swims through the aether with a speed of 186,830 miles a second. The aether was flowing through the laboratory like a river past its banks. The light-wave was divided, by partial reflection at a thinly silvered surface, into two parts, one of which was set to perform the up-and-down stream journey and the other the across-stream journey. When the two waves reached their proper turning-points they were sent back to the starting-point by mirrors. To judge the result of the race, there was an optical device for studying interference fringes; because the recomposition of the two waves after the journey would reveal if one had been delayed more than the other, so that, for example, the crest of one instead of fitting on to the crest of the other coincided with its trough.

To the surprise of Micwinning-posthelson and Morley, who conducted the experiment, the result was a dead-heat. It is true that the direction of the current of aether was not known—they hoped to find it out by the experiment. That, however, was got over by trying a number of different orientations. Also it was possible that there might actually be no current at a particular moment. But the earth has a velocity of 18 1/2 miles a second, continually changing direction as it goes round the sun; so that at some time during the year the motion of a terrestrial laboratory through the aether must be at least 18 1/2 miles a second. The experiment should have detected the delay by a much smaller current; in a repetition of it by Morley and Miller in 1905, a current of 2 miles a second would have been sufficient.

If we have two competitors, one of whom is known to be slower than the other, and yet they both arrive at the winning-post at the same time, it is clear that they cannot have travelled equal courses. To test this, the whole apparatus was rotated through a right angle, so that what had been the up-and-down course became the transverse course, and vice versa. Our two competitors interchanged courses, but still the result was a dead-heat.

The surprising character of this result can be appreciated by contrasting it with a similar experiment on sound-waves. Sound consists of waves in air or other material, as light consists of waves in aether. It would be possible to make a precisely similar experiment on sound, with a current of air past the apparatus instead of a current of aether. In that case the greater delay of the wave along the direction of the current would certainly show itself experimentally. Why does light seem to behave differently?

The straightforward interpretation of this remarkable result is that each course undergoes an automatic contraction when it is swung from the transverse to the longitudinal position, so that whichever arm of the apparatus is placed up-stream it straightway becomes the shorter. The course is marked out in the rigid material apparatus, and we have to suppose that the length of any part of the apparatus changes as it is turned in different directions with respect to the aether-current. It is found that the kind of material—metal, stone or wood—makes no difference to the experiment. The contraction must be the same for all kinds of matter; the expected delay depends only on the ratio of the speed of the aether current to the speed of light, and the contraction which compensates it must be equally definite.

This explanation was proposed by FitzGerald, and at first sight it seems a strange and arbitrary hypothesis. But it has been rendered very plausible by subsequent theoretical researches of Larmor and Lorentz. Under ordinary circumstances the form and size of a solid body is maintained by the forces of cohesion between its particles. What is the nature of cohesion? We guess that it is made up of electric forces between the molecules. But the aether is the medium in which electric force has its seat; hence it will not be a matter of indifference to these forces how the electric medium is flowing with respect to the molecules. When the flow changes there will be a readjustment of cohesive forces, and we must expect the body to take a new shape and