798 



NATURE 



[February 17, 1921 



y-- 



unaltcred is speed, for he is allowed to compensate 

 every confusion about space by an equal opposite 

 confusion about time. However, he is providea 

 with an instantaneous camera for taking snap- 

 shots which he can afterwards study, and he does 

 his best ; he makes his observations of times and 

 distances, and records them with dashed letters. 

 Meanwhile the other more comfortably situated 

 observer, attached to the slab and the laboratory 

 furniture (who also considers himself at rest, 

 though the first man may think of him as rushing 

 through the aether), records, undashed, the read- 

 ings of his peculiar instruments too. 



A relativist, not caring in the least which or 

 whether either of these sets of measurements has 

 any absolute meaning, but assuming them to be 

 made accurately, applies the transformation of 

 Lorentz and Larmor for change of co-ordinates 

 between sets of axes moving relatively to each 

 other; and thereby finds that if the laboratory 

 readings are x and t, while the flying man's read- 

 ings are x' and t' (each being supposed to have a 

 local space and time of his own, absolute space 

 and time having no meaning), the following rela- 

 tions must hold — 



x-vt , t - vxjc* 



From these simple but important, and indeed 

 fundamental, equations it comes out that if 

 x'/t' = c for the flying man, then xjt^c for the 

 other observer likewise. So the result is just 

 as if nothing at all was moving, except 

 light, and in fact as if bodily motion through 

 the light-conveying medium were meaningless. 

 Hence everybody should be satisfied, with- 

 out any appeal to, or confirmation of, any 

 physical theory whatever. The null (or dull) 

 result of the experiment now requires no 

 explanation ; there is no need even to emphasise 

 the double to-and-f ro journey of the light ; single 

 journeys serve ; for the apparent speed of light 

 is (really, has been assumed) the same in all direc- 

 tions, no matter what it be referred to. Distances 

 and times may appear different to different ob- 

 servers, but they are arbitrary or conventional 

 appearances at best, and they tend to compensate 

 each other. 



Hence arises the r — ct and r' = cV superstition, 

 about the concentricity of a wave front round each 

 one of a group of observers initially at the origin 

 however much they may have scattered since ; 

 because, apart from gravitation, x* + y''- + z^ — cH^ 

 must be independent of axes of reference ; or, 

 what is the same thing in our simple case, 



x—ci x'+cf, ^ ^ 

 .-^^ ,'= constant 



x'-cf x+ct 



_ f c-v 



And the other peculiarities of the simpler theory 

 of relativity immediately follow : some of them 

 very surprising and interesting. 



For instance, take the composition of motions : 

 If a thing is moving with speed u = x' jt', rela- 

 tively to an origin which itself is moving in (say) 

 the same direction with speed v referred to a fixed 

 NO. 2677, VOL. 106] 



origin, then the resultant speed w = x/t, referred 

 to the same fixed origin, will be obtained by aid of 

 the above transformation for moving axes reduced 

 to relative rest — 



x-ff{x +vt) ; /=/3(/ +vx'/c*) : 

 whence we get 



X 



w= - =- 

 t 



u+v 



I + uv/c* 



a curious expression for the combined velocities. 

 [Likening it to a rotation of axes, witht'/c = tanh d, 

 the summation is not tanh flj -f tanh 6^ but 

 tanh(flj-f- 6*2).] It gives simple summation for slow 

 speeds, and an unattainable maximum c for high 

 speeds. If either or both of the component velo- 

 cities attain the magnitude c, the resultant w 

 attains the same maximum, and cannot exceed it. 

 But the most notable property of this expression 

 is that it gives practically the same expression as 

 Fresnel's aether-intuition gave, for light travelling 

 down a stream of water — an expression verified 

 by Fizeau's famous experiment. For let the 

 speed u be that of light inside a dense material 

 medium, say c-^fi, and let the material medium 

 be itself travelling in the same direction at speed 

 V, then the resultant speed of the light would be, 

 by the above expression, 



■w= f:— , 



or, what is the same thing, 



7V = C u + v. !f- 



l+v/liC 



And this, to a high degree of approximation, is 

 practically identical with the Fresnel-Fizeau result, 

 viz. : 



■w = cjn -f- z'( I - I //i'). 



That such a result — which was supposed to give 

 some kind of information about the behaviour of 

 aether inside dense matter — can be obtained irra- 

 tionally by a simple geometrical device, is surely 

 surprising. 



Again, the variation of the mass factor in 

 momentum, which was originally predicted from 

 the electrical theory of matter and afterwards 

 verified, exhibits itself as an outcome of the rela- 

 tivity expression without any physical theory at 

 all. The inertia of an electric charge, and indeed 

 of all energy, seems to come out likewise. Light 

 has a mass-factor, but not a conserved or invari- 

 able one, while matter has both a fixed and a 

 variable term in its factor ; w-hich is a notable 

 and suggestive pair of facts. 



From the point of view of the above relativity 

 composition of velocities, the Michelson-Morley 

 result is obvious ; for if the speed u under observa- 

 tion is already c, as it is in that experiment, it is 

 useless to compound another velocity, zLv, with it ; 

 because, if that is the law of composition, the 

 resultant velocity still comes out c, no more and 

 no less. 



It may be said that whereas most experimenters 

 assume an absolute time, the relativist assumes 

 one absolute unattainable or unexceedable velo- 



