GRAVITATION AND RELATIVITY Since all the phenomena of light and of electromagnetism are believed, on almost incontrovertible evidence, to he in accordance with the hypothesis of relativity, it is necessarily impossible to determine absolute velocity by optical or gravitational means. On the other hand, as we have already mentioned, the Newtonian law of gravitation is readily seen to be inconsistent with the hypothesis of relativity. Three alternatives are open : (i.) The Newtonian law may be true, in which case it must be possible to determine absolute velocity by gravitational means.
(ii.) The Newtonian law may be untrue in its original form, but may become true when amended so as to conform to the relativity hypothesis.
(iii.) Neither of the foregoing possibilities may be true.
Alternative (i.) was explored by Sir Oliver Lodge, who, assum ing the exact truth of the Newtonian law of gravitation, deduced that the observed motion of the perihelion of Mercury could be accounted for if the sun were moving through space with a ve locity of about 7okm. a second in a certain direction. This investi gation had to be abandoned when Eddington pointed out that a similar discussion of the motions of the other planets would lead to vastly different values for the sun's velocity. Alternative (ii.) was explored by Einstein and others, but was found to lead to a motion of the perihelion of Mercury equal only to one-sixth part of that actually observed.
Alternative (iii.) remained with its innumerable possibilities.
Einstein commenced his attack on the problem by eliminating all possibilities which did not conform to two general principles. The first of these was the principle of relativity. Inasmuch as all physi cal phenomena except gravitation were believed to conform to this principle, it was natural to try, as a working hypothesis, the effect of assuming gravitation also to conform. The second principle was the so-called principle of equivalence, and this demands a word of explanation. _ To our children we explain that an apple falls to the ground be cause a force of gravitation inherent in the earth's mass impels the apple towards the centre of the earth. Most schoolboys know that this is not quite the whole story; the path of the apple is more accurately determined by supposing the apple to be acted on simultaneously by two forces—a gravitational force of attraction towards the earth's centre and the centrifugal force arising from the earth's rotation. It is only because the earth's rotation is com paratively slow that the conception of an attraction towards the earth's centre gives a tolerably plausible account of the fall of the apple. If the earth rotated at 17 times its present rate objects
would not fall, even approximately, towards the earth's centre; they would fall always parallel to the earth's axis, and the inhabi tants of the northern hemisphere might explain this as arising from a force of repulsion inherent in the pole star. If the earth rotated many times faster even than this, bodies would fall always per pendicularly away from the earth's axis, and this might be inter preted as arising from a gravitational repulsion residing in the earth's axis.
These illustrations will show that it is easy to confuse accelera tion arising from the earth's rotation with gravitational attraction. We may go further and say that it is impossible to distinguish be tween the effects of gravitational attraction and the effects of ac celeration of any kind whatever. Every aviator knows this to his sorrow; it is inherently impossible to devise any instrument which shall show the direction of the vertical in an aeroplane, since an acceleration of the aeroplane produces on any instrument what ever, effects which are indistinguishable from those of gravity. From such considerations Einstein was led to his principle of equivalence, which may be enunciated as follows : "A gravitational field of force at any point of space is in every way equivalent to an artificial field of force resulting from accel eration, so that no experiment can possibly distinguish between them." Guided by these two principles—relativity and equivalence— Einstein was led to the view that all gravitational "fields of force" must be illusions. The apparent "force" arises solely from acceleration and there is no other kind of gravitational force at all. In this statement, as in the statement of the principle of eauivalence above, the word acceleration is used in its widest sense. Acceleration results not only from change in the amount of a velocity, but from a change in its direction also. For instance a motor-cyclist riding in a circle at a uniform speed of 6o miles an hour will be the subject of an acceleration towards the centre of the circle. He knows that the apparent force so produced is just as real in its effects as gravitation, and to save himself from falling as a result of its influence he must incline the direction of his machine to the vertical.