March 



1918] 



NATURE 



'Htm 

 up\i 



is k 



HThaps best 

 Huid filling 

 iini, niil ;is 

 . >,.;hv ;.n.l 



own as til,, 

 a phvsic-al 



;)ii). In s(. 



iiiework of reffrcnci' in -[)a(f. WC 

 lure the a?ther as a toLn -ilimcnsic 

 iformly .Minkowski "s sjjacf-tinif 

 iiaterial three-ciimcnsional lluid (h 

 !<• independently. 



I'he {X)sition we ha\r now rrarlir 

 iiciple of relativity, in -o far ; 

 ory, it seems to be .luiply coniir 

 loriments (except in regard to l; 

 as it is a philosophical theory, it i> no nior<- iban a 

 itimate and useful point of view. 1 now pass on lo 

 ^•neralised principle of relativity, in which we nnisi 

 ontent at first to be guided by a natural generalisa- 

 n of these results, hoping- lalei- lo \u- able to checl< 



tentative conclusions by expcrinit nt. 



1 f we analyse any scientific obserx aiion, distinguish- 



, between what we perceive and what we mereh 



■r, it always resolves itself into a coincidence in 



1 (■ and time. A physicist states that he has ob- 



ed that the current through his coil is 5 milli- 



peres ; but what he actually saw was that the image 



wire thrown by his gah ani)mt i«r coincided with a 



lin division on a iScale. 1 It- mt asures the tempera- 



of a liquid, but the observation is the coincide )iiC 



"le top of the mercury with a division on th( 



IOmeter. If then we had to sum up 



•hole of our experimental knowledge, we should 



to describe it as consisting of a large number of 



idences. 



: complete history of the progress of a particle con- 

 of a knowledge of its path and the time at which 

 :upied each point of the path. The time may be 

 ied as an extra co-ordinate corresponding with a 

 th dimension, and so the whole history may be 

 led up b}' a line in four dimensions representing 

 ^particle's progress through space and time. We 

 this four-dimensional line the world-line of the par- 

 ticle. Imagine that we have drawn the world-lines of 

 all the particles, light-waves, etc., in the universe : we 

 shall then have a complete history of the universe. It 

 will be a rather dull history-book ; the Venus of Milo 

 " 'M be represented by an elaborate schedule of measure- 

 its, and Mona Lisa by a mathematical specification 

 lie distribution of paint; still they are there, if only 

 w ' c.^n recognise them. I have here a history of the 

 universe — or part of it. Unfortunately I was not able 

 ! ilraw it in four dimensions, and even three dimen- 

 is presented difficulties, so I have drawn tbo w orld- 

 N in two dimensions on the surface of a football 

 Ider. 



\ great deal is shown In i . wliiih, properly speak- 

 ^, is not history at all, bccausr \\ is necessarily out- 

 side experience. As we have seen, it is only coinci- 

 dences — the intersections of the world-lines — that con- 

 stitute observational knowledge; and, moreover, if is 

 tiot the place of intersection, but the fact of ini( r- 

 section that we observe. I am afraid the two-dimen- 

 sional model does not give a proper idea of this, be- 

 cause in two dimensions any two lines are almost 

 bound to meet sooner or later; but in three dimensions, 

 and still more in four dimensions, two lines can, and 

 usually do, miss one another altogether, and the ob- 

 servation that they do meet is a i^cniiinc adilifion to 

 knowledge. 



When I squeeze the bladdci- ibc worhl-liius are bent 

 about in different ways. Bui I have not altered the 

 history of the universe, because no intersection is 

 ^rented or destroyed, and so no observable event is 

 ! ed. The deformed bladder is just as true a history 

 Nature as the undeformed bladder. The bladder , 

 represents Minkowski's space-time world, in which I 

 the world-lines were drawn ; so we can squeeze Min- | 

 kowski's world in any way without altering the course I 

 of e\ents. Wo do not usuallv use the common word 



•■squeeze"; we call it a uialhcittutunl lraiist<)r)n(itioii. 

 but it means the same thing. 



The laws ol Nature in their most general form 

 nnisi (Usrribe (i)irectl\ the behaviour of the world- 

 lines in <itliei- the uniiistorled or the distoi^ted motlel, 

 lierause it is indifleiinl wtiiili we take a^ 'he true 



important i)rinei|)li- ; but, heini^ alniosi a truism, il 

 does not in itseM' help us lo diierniine the laws of 

 Nature without making some additional hypothesis. 

 'J'here is one law — the law of gravitation — which espe- 

 cially attracts our attention at this point, and we shall 

 look into it more closely. 



We know thai one particle attracts another particle, 

 and so intluences the history of its motion. This 

 evidently means that one world-line will deflect any 

 other w'orld-line in its neighbourhood. Apart from this 

 influence, the world-line runs straight, bending neithei 

 to the right nor to the left, provided the bladder is in 

 its undistorted state, i.e. provided we use Minkowski's 

 original space-time. That is not so much a matter 

 of observation as of definition. It defines what we are 

 to regard as the undistorted state, though ii is by 

 observation that we learn that it is possible to find a 

 s|)ai('-time in which the world-lines run straight when 

 undisturbed bv ifravitational or other forces. I must 

 own thai there i< a certain logical difficulty in saying 

 that a wH>rld-line runs straight when there are no 

 others near it; because in that case there could be no 

 inter.sections, and we could learn nothing about its 

 course by observation. However, that is not a serious 

 difficulty, though you may be reminded of the sage 

 remark, "If there were no matter in the universe, the 

 law of gravitation would fall to the ground." 

 (7e /'c continued.) 



lXI]-h:RSri] AXD 1:1)1 CATIONAL 



i.\"rELLii;i-:.\(K. 



The Times announces that .Senator Dennis has given 

 12,000/. to Dalhousie L niNcrsity for a chair of political 

 science in memory of his son, ('apt. l-aic Dennis, who 

 was killed at Vimy Ridge; and tha.i Major V.. A. de 

 Rothschild, who died at Cairo from wounds on Novem- 

 ber T7, aged thirty-one, has left the sum of 5oo(jf. to 

 Harrow School for a scholarship, the conditions of 

 w hich are to be approved by his brother Anthony. 



Iiii. Department of Agriculture and Technical In- 

 siiueiion for Ireland has issued its programme of 

 suninier courses of instruction for teachers to be held 

 this \ear. The courses will, with the exception of ilu- 

 courses of instruction in rural science (including school 

 gardening) for National School teachers, begin on July 

 2, and close on July 26. The courses in rural science 

 (including school gardening) will begin on .\ugust (1, 

 and close on August 30. IVachers who attend i)i<- 

 courses refndarh- will be allowed a sum of :;/. ui.v. 

 towards their exp<-nsi's while living at the c-(Mitri'. .and 

 third-class railway fare for one return journex from 

 the railway station nearest their school or centre. 

 Among the subjects in which courses have been ar- 

 ranged are the chemistry of engineering materials, 

 technology for tc^achers, <'xperimental scii nee, domestic 

 science, and rural science. The courses ,ne opt'ii only 

 to those who are alx^)ve twenty years of age, and, except 

 in certain cases, only to teachers who are engaged 

 (a) by local committees of technical instruction, or {h) 

 in schools receiving grants either directlv from th<' 

 Department or under the i)ro\ isions of an approved 

 local scheme of technical instruction. 



The annual report of InixcrsitN Collogi, London, 

 shows that whereas in normal times tlie total numbel- 

 of studi-nts, d.i\ ,ind e\-ening, amounts to .about jjoo. 



2^27,, VOL. lOl] 



