February 12, 1920] 



NATURE 



631 



THE THEORY OF RELATIVITY. 

 ' I ""HE meeting- of the Royal Society on Feb- 

 -l- ruary 5 was devoted to a discussion on the 

 theory of relativity. It was opened by Mr. J. H. 

 Jeans, who said it was a better analogy to liken 

 the new principle, not to a key of the universe, 

 but to a ward in its lock, which gave direction 

 to the efforts made to open it, admitting some 

 and excluding others. In this respect it resembled 

 the doctrine of the conservation of energy and 

 the second law of thermodynamics. Where any of 

 these gave a positive result it was because a 

 process of exhaustion showed that anything else 

 would lie impossible. 



The foundation of the theory may be considered 

 to have been laid by Einstein's hypothesis, put 

 forward in 1905, that light from any source 

 appears to any observer to travel with the same 

 velocity C ; this hypothesis was founded on the 

 Michelson-Morley experiment, and has since been 

 confirmed by that of Majorana; it also explains 

 a number of physical phenomena. It can best be 

 visualised by the idea that to each observer the 

 wave-surface is spherical in the four-dimension 

 continuum. Then x'^ + y^ + B^ + {iCtf (radius for the 

 first observer) transforms into an identical ex- 

 pression with accented letters (radius for the 

 second observer) by a rigid-body rotation. Such 

 a rotation would resolve pure time into partly 

 time, partly space, and vice versa. The following 

 is an example of this : Suppose that a man lives 

 seventy-five years, and dies 1000 miles from his 

 birthplace ; then to an observer on a rapidly 

 receding- star he might appear to have lived 

 seventy-six years and travelled billions of miles. 

 (In reply to Prof. Newall, who imagined paper 

 screens to be erected at a distance of 100 light- 

 seconds from the orisrin, from which a flash of 

 light is emitted, and from which one of the 

 observers moves while the other remains, Mr. 

 Jeans admitted that the former would not see the 

 reflections simultaneously, the reason being that 

 the screens would not lie on a four-dimensional 

 sphere to him.) This conception was preferable 

 to that of the Lorentz contraction, which pre- 

 sented grave difficulties in the case of a rotating 

 wheel, the axis of which is at rest in the Eether ; 

 the rim would undergo contraction, while the 

 spokes would remain unaltered. 



Mr. Jeans used the following analogy to explain 

 the nature of Einstein's latest theory. Imagine a 

 race of men who had spent all their lives in caves. 

 They would be in ignorance of the earth's rotation, 

 and would consider gravity as a force constant in 

 direction ; however, two experiments might reveal 

 the fact of rotation to them. If they set a ball 

 swinging in an ellipse, by a long string, the apse 

 of the ellipse would move ; moreover, delicate 

 measures would show that the course of rays of 

 light was not quite straight relatively to their 

 rotating framework. This is closely analogous to 

 the observed progression of Mercury's perihelion 

 and to the deflection of light-rays by the sun ; in 

 each case "we have tacitly assumed fixed axes 

 NO. 2624, VOL. 104] 



where nothing is fixed : we have formed wrong 

 ideas of the nature of gravitation, and our defini- 

 tion of a straight line is interwoven with the 

 ideas of an untrue system of geometry." 



The reason why the new law of gravitation can- 

 not be put in simple form is that there is no force 

 of gravitation ; the laws of motion can be put in 

 the simple form Sfds = o. There are, however, 

 two ways of defining ds. Einstein defines it as a 

 line-element in a distorted space-time continuum. 

 This necessarily involves the spectral shift to the 

 red, and an objective curvature of space. It may 

 also be simply defined as a conventional alge- 

 braical symbol given by Einstein's equation, but 

 without assuming his physical interpretation ; in 

 this manner it is possible to deduce the two astro- 

 nomical effects already verified, while leaving- the 

 shift of spectral lines undetermined. Decisive 

 evidence for or against the spectral shift would 

 be a guide as to the adoption of one or other 

 definition of ds. 



Prof. Eddington compared Euclidean space to 

 a picture in a framework of rectangular co- 

 ordinates, and Einstein's space to a map with 

 curved lines of latitude and longitude. Just as 

 the map could not accurately represent the earth's 

 surface, unless it was made on a curved surface, 

 so Euclidean space could not contain an accurate 

 representation of the space-time continuum. We 

 could look on Einstein's law of gravitation as 

 giving instructions for the joining together of 

 successive elements of space. The law must in- 

 clude all the laws of mechanics, including- the 

 conservation of energy and momentum. 



Space and time could be explored in two ways 

 — either by using clocks and measuring scales, or 

 by observing moving particles and light-waves. 

 The second method was both more elementary 

 and more sensitive. An example of it was the 

 search for the spectral shift. The reason for the 

 shift might be briefly given thus. The time of 

 vibration of a particle involves the factor 



f 2wV' 



which clearlv increases as r dimin- 



ishes, so that the vibration is slower on the sun 

 than on the earth. 



Sir F. W. Dyson spoke on the motion of the 

 perihelion of Mercury ; the observed centennial 

 motion exceeds that calculated on the Newtonian 

 law by 43", which is much the largest unexplained 

 quantity in planetary theory. \'arious attempts 

 have been made to explain it. An excess of |" 

 of the sun's equatorial radius over the polar would 

 suffice ; this amount is considered to be in excess 

 of what observation will admit ; the latter suggests 

 a slight excess of the polar radius ; moreover, such 

 an equatorial excess would produce a shift of 

 the orbit-plane of Mercury too great to be ad- 

 mitted. An unknown planet is excluded, since 

 it could not fail to have been seen or photo- 

 graphed at some of the total eclipses when such 

 a body has been specially looked for. A ring of 

 small planets would have to be in the plane of 

 Mercury's orbit, or it would produce an effect on 



