748 



NATURE 



[August ii, 192 i 



Remarks on Simple Relativity and the Relative Velocity of Light.^ 

 By Sir Oliver Lodge, F.R.S. 



II. 

 The Relative Velocity of Light. 



CONSIDER once more the assumption that is 

 either tacitly or confessedly introduced into 

 the establishment of the Larmor-Lorentz trans- 

 formation and the consequent composition of velo- 

 cities. 



It is this : that the velocity of light outside and 

 far away from matter is absolute ; in the sense that 

 it will be measured as the'same velocity by every 

 observer, no matter what his relation may be to 

 space and time — i.e. no matter where or when 

 he exists, or at what unknown speed he may be 

 moving, not even if his speed w^ere infinite. 



A very extraordinary idea that, and one difficult 

 to believe. It is true that it follows from the 

 equations previously written down by Larmor and 

 Lorentz, but they were originally limited to the 

 small range of u/c that covered all practicable 

 observations, and so were not meant to be of 

 universal application and pressed into infallible 

 consequences. The merit, or demerit, of Einstein 

 is that he had no such compunction, and was 

 ready to follow the argument whithersoever it 

 led ; and the result — made possible by his wonder- 

 ful grasp of recondite machinery which he annexed 

 from pure mathematicians, especially recondite 

 when gravitation was included — was a far-reaching 

 effort towards a universal synthesis, in the course 

 of which a few definite features amenable to 

 observation emerged — with the known brilliant 

 results. 



Now that the velocity of light in free aether is 

 constant is admitted by everybody, the only 

 reasonable alternative would be some dependence 

 on wave-length, which would mean that the aether 

 was coarse-grained ; and that is experimentally 

 negatived by several phenomena and by all 

 manner of determinations of what used to be called 

 a ratio of units, "7;," but is more intelligibly and 

 satisfactorily called a measure of the product of 

 the magnetic and electric aetherial constants ju,K. 



But that the relative velocity of light, deter- 

 mined by an observer travelling with speed w 

 to meet it, should still appear the same, and be 

 independent of hiis motion, is curious, not to say 

 paradoxical. The relative velocity of the observer 

 and the light must be c + u- — common-sense forbids 

 otherwise, — but if he seeks to measure it he will 

 get, we are told and inclined to believe, not c + u, 

 but (c + M)-f (i-f cw/c2), and that is simply c. 



So far as I know, no one has ever measured 

 the apparent velocity of light from a star or from 

 one of those spiral nebulae from which the earth 

 is receding at hundreds, or even thousands, of 

 miles per second. It is not easy to see how it can 

 be done, for the readily observed Doppler effect 

 is always attributed to relative motion of source 



1 Continued from p. 719. 



NO. 2702, VOL. 107] 



and observer ; and if those are relatively fixed it 

 has been definitely shown that no steady motion 

 of the medium has any observable influence on 

 either direction or frequency (Phil. Trans., 1893, 

 vol. clxxxiv. , p. 784). Gusts, however, cause 

 wailing ; and by utilisation of the variation of an 

 already occurring Doppler effect something may be 

 done {I.e., p. 785). But, in view of the univer- 

 sality of the above transformation equations, we 

 may admit that it is unlikely that any result other 

 than c will be obtained. It is by assuming the 

 velocity of light constant that the recession velo- 

 city is measured ; the whole observed retardation 

 is naturally attributed to relative velocity of source 

 and observer ; though if we could be sure that all 

 the observed relative velocity really belonged to 

 the receiver, and none of it to the source, we 

 should know that the reason we were able to 

 observe an apparent change in frequency was 

 because of the resultant speed at which we received 

 the waves. But that is just the difficulty — we 

 cannot tell how much of the recession belongs to 

 the source and how much to the receiver. If we 

 could know the observer's speed through the 

 aether we could clearly say that he met the waves 

 more slowly or more quickly than he would other- 

 wise get them ; and this reasonable statement has 

 never been disproved by observation. 



We ought not to claim, therefore, as some 

 philosophers do, that the fundamental hypothesis 

 of Einstein about observed velocity of light has 

 been directly verified and is a sound basis on 

 which to found a theory. The hypothesis does 

 not justify any theory, though a successful theory 

 may justify the hypothesis. A mistaken claim for 

 what has been done by experiment is often made ; 

 and as clear statements are always valuable, 

 whether right or wrong, I select for quotation 

 one from Lord Haldane's recent book, "The 

 Reign of Relativity," on p. 82 : — 



Long before 1905 it had been found by experiment 

 that the velocity of light appeared to be always 

 186,330 miles per second, whether the passage of its 

 rays was towards us while we were at rest with 

 regard to its source, or whether we were ourselves 

 moving towards that source. 



Now whether what is here asserted to have 

 been "found by experiment" about the velocity 

 of light be a fact or not, no observation of a 

 discriminating kind had been made before 1905 ; 

 and I would myself deny that any such observa- 

 tion has been made since. Certainly no experi- 

 ment of the direct kind suggested in this quotation 

 has ever been made^ — it is doubtful if it can be 

 made. Every purely terrestrial measurement 

 of the velocity of light has been made, and must 

 necessarily be made, on light which has travelled 

 round a contour, or, what is the same thing, 

 which has gone and returned over the same path. 

 Such an experiment proves nothing, either for 



