34 



NATURE 



[March 14, 1918 



professors with fourteen assistant lecturers, and the 

 students in all departments were 556 in 19 16. The 

 fees for instruction are 30 francs for each semester, 

 tog"ether with certain special fees, and foreigners are 

 charged treble fees. The six schools have a total of 

 2427 students, and are fully equipped with laboratories 

 for experimental instruction. On leaving these schools 

 the students enter the Union of Swiss Technicians, 

 which association now counts its members by thousands 

 and has for its organ the Swiss Technical Review, 

 which publishes much good original work. Altogether 

 these institutions have proved a great success and 

 have been of material benefit in training a large body 

 of men for the industries, many of whom have after- 

 wards qualified for high industrial or administrative 

 positions at home or abroad. 



GRAVITATION AND THE PRINCIPLE OF 

 RELATIVITY.'^ ■ 



II. 



\\T E have to admit, then, that a world-line can be 

 * * ibent by the proximity of other Avorld-lines, It can 

 also be bent, as you see, by the proximity of my 

 thumb. The suggestion arises. May not the two 

 mod^s of bending be essentially the same? The bend- 

 ing by my thumb (a mathematical transformation of 

 space and time) is in a sense spurious ; the world-line 

 is pursuing a course which is straight relative to the 

 original material. Or we may perhaps best put it this 

 way — the world-line still continues to take the shortest 

 path between two points, only it reckons distance 

 according to the length that would be occupied in the 

 unstretched state of the bladder. It is suggested that 

 the deflection of a world-line by gravitation is of the 

 same nature ; from each world-line a state of distortion 

 radiates, as if from a badly puckered seam, and anv 

 other world-line takes the shortest course through this 

 distorted region, which would immediately become 

 straight if the strain could be undone. The same rule 

 — of shortest distance as measured in the undistorted 

 state — is to hold in all cases. This is a mode of 

 reasoning which has often been fruitful in scientific 

 generalisations. A magnetic needle turns towards the 

 end of a bar-magnet; it also turns towards a spot near 

 the pole of the earth; hence the suggestion that the 

 earth is a magnet. We assume the essential identity 

 of the two modes of deflecting the needle. It is a 

 daring step to apply the analogy and assume the essen- 

 tial identity of the two ways of deflecting world-lines ; 

 but at any rate we shall make this assumption and see 

 what comes of it. 



You will see that according to this view the earth 

 moves in a curved orbit, not . because the sun exerts 

 any direct pull, but because the earth is trying to find 

 the shortest way through a space and time which have 

 been tangled up by an influence radiating from the 

 sun. We can continue to describe this indirect influ- 

 ence of the sun on the earth's motion as a "force"; 

 but, assuming that it makes itself felt as a modification 

 or strain of space and time, we are able to bring the 

 discussion of the laws of this force into line with the 

 discussion of the laws of space and time, i.e. the laws 

 of geometry. Needless to say, we could not determine 

 a physical law like the law of gravitation by geo- 

 metrical reasoning without making some assumption. 



I am afraid that to talk of a force as being a dis- 

 tortion of space and time must at first appear to you 

 hopeless jargon. But it must be remembered first that 

 \ye are not concerned with any metaphysical space and 

 time. We mean by space and time simply a'scafifold- 



1 Discourse delivered at the Royal Institution on Friday, February i by 

 Prof. A. S. Eddington, F.R.S. Continued from p. 17. ' 



ro. 2524, VOL. lOlJ 



ing that we construct as the result of our measures ; 

 and if anything queer happens to our measuring appa- 

 ratus, the scaholding may easily go crooked, faking 

 our everyday conception of space, we should say thai 

 this room is at rest ; we have been told that it is being 

 carried round the earth once a day, but in practical life 

 we never pay any attention to that. The space that 

 we naturally use is thus different from, and it is not 

 difficult to show that it is distorted as compared with, 

 the more fundamental astronomical space in which this 

 room is travelling at a great velocity. So our scaffold- 

 ing is crooked. But, it may be asked, in what way can 

 this distortion of our space-scaffolding be regarded as 

 a force? The answer is quite simple. We perceive 

 it as a force, and that is the only way in which we 

 do perceive it. We do not perceive that this room 

 is being carried round by the earth's rotation, but we 

 perceive a certain force— the earth's centrifugal force. 

 It is rather difficult to demonstrate this force, because 

 gravitation predominates overwhelmingly; but if 

 gravity were annihilated we should have to be tied 

 down to the floor to prevent our flying up to the 

 ceiling, and we should certainly feel ourselves pulled 

 by a very vigorous centrifugal force. That is our onh- 

 perception of the crookedness of our scaffolding. 



We often call the centrifugal force an " unreal " 

 force, meaning that it arises simply from a transforma- 

 tion of the framework of reference. Can we feel con- 

 fident that gravitation is in any sense more "real"? 

 In effect they are so much alike that even in scientific 

 work we speak of them in one breath. What is called 

 the value of gravity in London, 981-17 cm./sec.=, is 

 really made up partly of the true attraction of the 

 earth and partly of the centrifugal force. It is not 

 considered worth while ' to make any distinction. 

 Surely, then, it is not a great stretch of the imagination 

 to regard gravitation as of the same nature as centri- 

 fugal force, being merely our perception of the crooked- 

 ness of the scaffolding that we have chosen. 



If gravity and centrifugal force are manifestations 

 of the same underlying condition, it must be possible 

 to reduce them to the same laws ; but we must express 

 the laws in a manner which will render them com- 

 parable. There is a convenient form of Newton's law, 

 which was given by Laplace and is well known to 

 mathematicians, which describes how the intensity at 

 any point is related to the intensity at surrounding 

 points — or, according to our interpretation, how the 

 distortion of space at any point fits on to the distortion 

 at surrounding points. It is evidently an attempt to 

 express the general laws of the strains in space and 

 time which occur in Nature. If we are correct in our 

 assumption that gravitation involves nothing more than 

 strain of space-time,^ so that its law expresses merelv 

 the relation between adjacent strains which holds bv 

 some natural necessity, clearly the strains which give 

 the centrifugal force must obey the same general law. 

 Here a very interesting point arises. We cannot recon- 

 cile the Newtonian law of gravitation with this condi- 

 tion. Newton's law and the law of centrifugal force 

 are contradictory. 



To put the matter another way, if we determine the 

 strains by Newton's law, we get results closely agree- 

 ing with observation, provided Minkowski's space-time 

 is used ; but if we avail ourselves of our right to use a 

 transformed space-time, the results no longer agree 

 with observation. That means that Newton's law in- 

 volves something which is not fully represented bv 

 strains, and so does not agree with our assumption. 

 We must abandon either our assumption, or the 

 famous law which has been accepted for more than 



2 The idea is that matter represents a seam or nucleus of stmn, and the 

 strains at other points link themselves on according to laws inherent in the 

 contznuum and qu-te independent of the matter. The matter sta- ts the strain. 

 but does not control it as it goes outwards. 



