7i6 



NATURE 



[August 4, 192 1 



Remarks on Simple Relativity and the Relative Velocity of Light 

 By Sir Oliver Lodge, F.R.S. 



I. 



IN continuation of my article in the Relativity 

 Number of Nature (vol. cvi., p. 795, Feb- 

 ruary 17, 1921), I propose to discuss more fully, 

 and to express as clearly and simply as possible, 

 some of the points on which philosophic disciples 

 or expounders of Einstein have written, so as 

 perhaps to remove a certain amount of misappre- 

 hension, and incidentally to set my own views 

 before other physicists, in order that they may be 

 controverted where necessary. On some other 

 points of more general interest I have written in 

 the Fortnightly Review for next September, espe- 

 cially on the foundation which had been laid by 

 Einstein's predecessors before the philosophic 

 doctrine of relativity was made definite and 

 erected into a comprehensive physical theory. 

 The Fundamental Relativity Hypothesis. 



Einstein's first fundamental assumption is that 

 direct observation of our absolute motion through 

 space is not only unachieved, but also in the nature 

 of things impossible ; wherefore it can be held that 

 such motion has no intelligible meaning. Those 

 who admit an aether prefer not to shut the door 

 on inquiry, but meanwhile express their provisional 

 agreement by saying that its various functions and 

 properties are so uniform, so universal, and so 

 interrelated, that observation of any suspected 

 effect of motion through the aether is liable to be 

 frustrated or negatived by some — so to say — in- 

 evitable opposite effect ; and that the compensa- 

 tion, at any rate over a wide range, is complete. 



Einstein's second fundamental assumption is 

 that the one absolute quantity which can be 

 observed, namely, the velocity of light — if it be a 

 velocity — is unique and so fundamental that every 

 observer must necessarily measure the same result 

 if he make his measurements correctly, no matter 

 what his own motion may be ; which, after all, is 

 only another way of saying that his own motion 

 through the aether is pragmatically a meaningless 

 expression. 



It is not claimed that these assumptions, which 

 are certainly consistent with the ■ Larmor-Lorentz 

 transformation equations — at least, when they in- 

 clude the factor jS, expressive of the FitzGerald- 

 Lorentz contraction — are really established by 

 them. That would be reasoning in a circle. Nor 

 do the equations necessarily substantiate any meta- 

 physical assertions about time or space or aether; 

 but they do lead to algebraic and legitimate deduc- 

 tions. 



The Time and Space Transformation. 

 The importance of those transformations- — cor- 

 relating the states of the same material system 

 travelling at different speeds — can scarcely be 

 exaggerated. They have been arrived at in many 

 ways, usually by aid of ideal and hypothetical and 

 apparently impossible experiments, sometimes by 



NO. 2701, VOL. 107] 



considering that an event does not effectively 

 happen until we have seen it happen, thus entail- 

 ing relative delay; and they have been variously 

 interpreted. The original gist of the equations 

 was that a moving observer must not only take his 

 distances as variable; he must consider his times 

 variable too. He must have a local and fictitious 

 time peculiar to himself, if he is to ignore his own 

 motion and treat his direct measurements as con- 

 clusive. 



Einstein's step was equivalent to dispensing 

 with any overt fiction about this subjective or local 

 measure of time, to claiming that it was as real as 

 any other, though peculiar to each observer, and 

 to seeing what emerged. 



Now if we agree to waive any question of ex- 

 perimental practicability, and proceed in an ideal 

 fashion, it is easy enough to obtain notions about 

 the required transformation ; and as I have not 

 seen the equations obtained so directly or naively, 

 I proceed to deduce them thus : — 



A stationary observer, supposed able to time the 

 passage of light from a source at a distance x, may 

 be expected to get the result 



If he be moving towards the source with speed u, he 

 will be relieving the light of some of the journev by 

 doing that bit himself. The light need now only 

 travel a smaller distance x' to meet him, and the 

 observer will have travelled the remainder, namely, 

 x — x'. So if the time taken on the jointly performed 

 journey be /', and if he finds it possible to measure 

 the distance x' at the instant the light reaches him, 

 which is evidently the right moment, he will get 



y 



and 



,=L as the speed of the light. 



r-y 



:_ ___ =u as his own speed. 



Given these three equations, we get by mechanical 

 algebra without further reasoning 



/ = / + ^, 



as well as the more obvious 



x=x' + ui\ 



without mentioning relativity at all. 



If all these measurements could be really made, we 

 should have 



and u could be determined in terms of c. But the 

 measurements are impracticable as they stand, for 

 how is an observer to know the instant at which a 

 particular portion of light left the source? In other 

 words, how Is he to time an event on the source 

 when he is dependent on the light itself for informa- 

 tion of its occurrence? He might have the event tele- 

 graphed, but that information also is transmitted by 

 the aether at the same pace. So the foiled inquirer 

 will naturally try to get some additional data by 

 reversing his motion and starting back again from 



