8o8 



NATURE 



[February 17, 192 1 



"Space, Time, and Gravitation." This principle 

 states that there are relations between the coeffi- 

 cients in the formula for ds- which hold, no matter 

 what system ol co-ordinates is chosen. Edding- 

 ton regards the co-ordinate system as decided 

 upon arbitrarily, having no real physical impor- 

 tance, and always eliminating itself in any actual 

 physical process, while the only thing that has 

 physical importance is space-time, which he treats 

 on purely geometrical lines. From this point of 

 view the principle is evidently correct ; but it is 

 not the point of view of physics. In physics the 

 co-ordinate systems actually chosen are adopted 

 entirely because they give specially simple forms 

 to relations between measured quantities, and thus 

 are not chosen arbitrarily. It woul3 therefore be 

 conceivable, and indeed not improbable, that 

 there could be no relations between the g-'s that 

 would not have special forms with ordinary co- 

 ordinate systems. On the other hand, the pro- 

 perties of space-time never appear in physical 

 laws ; thus it is space-time that eliminates itself 

 when the problems are reduced to terms of 

 measurement, and the irrelevance of the mesh- 

 system is a proposition, not about the unimportance 

 of convention, but about physical measurements 

 themselves. Hence it is a part, not of geometry, 

 but of dynamics, and can be arrived at only by 

 extension. Now that the predictions of the theory 

 have been verified, the proper course to adopt is 

 to derive the form of di^ from the experi- 

 mental results that these express, and to regard 

 the principle as an interesting experimental result. 



Einstein's own presentation differs somewhat 

 from Eddington's, but is also open to some objec- 

 tions. In his "Relativity, the Special and the 

 General Theory " (English translation) Einstein 

 states on p. 2 that he uses the term " geometry " in 

 its usual sense of the logical connection of ideas 

 (? propositions)" among themselves. Then, on 

 p. 3, he introduces the further proposition that 

 two points on a practically rigid body always 

 correspond to the same distance, however the 

 bodv may be displaced, and considers that this 

 converts geometry into a branch of physics. This 

 is not the case ; it can only give series of implica- 

 tions between propositions of the truth of which we 

 are ignorant, until some of these propositions have 

 been proved by sensory experience, which is not 

 a part of geometry ; they afso require a process of 

 generalisation to yield results of sufficient 

 generality to form the basis of a geometry, so 

 that a science reached in this way must be 

 extensive. 



On p. 9 of his book, Einstein's attitude 

 towards "space" is closer to ours than to 

 Eddington's, for he resolves to shun the 

 word entirely, admitting that he cannot form 

 the slightest conception of its meaning, and 

 replaces it bv the notion of position (i.e. measured 

 position) relative to a practically rigid bodv of 

 reference. In the latter part of the book he 

 appears to regard space, not as a primary entity 

 of Nature, but merely as a conventional construct, 

 composed of the aggregate of all possible values 

 NO. 2677, VOL. 106] 



of the three position co-ordinates. In this form 

 the notion may be useful in theoretical work, but 

 we cannot attribute any ultimate physical impor- 

 tance to a thing we have constructed ourselves. 

 In fact, he makes it clear on p. bo that the prin- 

 ciple of relativity is a postulate to be tested 

 by experience : a suggestion offered as possibly 

 true, but with no a priori necessity about it. Its 

 validity, in the opinion of its author, rests wholly 

 on the success of its physical predictions. Con- 

 sequently, as was stated above, the correct pro- 

 cedure now is to deduce the theory from the facts 

 originally predicted by it, with whatever further 

 postulates may be necessary. 



Although we have criticised the chief current 

 expositions of the Einstein theory, it is the omis- 

 sion of physicists to provide any satisfactory 

 analysis of the foundations of their own subject 

 that is chiefly at fault, and the rcmedv is a proper 

 discussion of the relation of physical laws to ihe 

 observations on which they are founded, and of the 

 probability of inferences based upon them. 



We may devote some attention to the question 

 of the comparison of standards at different places, 

 which must play an important part in any theory 

 of measurement. Before the publication of the 

 special theory of relativity, the accepted view w'as 

 comparatively simple : the measured length of the 

 conventional rigid bar was supposed to be the 

 same however it was displaced and turned, and 

 the same applied to the period of vibration of a 

 clock or an atom (in the former case subject to 

 the known influence of temperature and gravity). 

 This gave a convenient basis for comparison of 

 standards, for all could be expressed in terms of 

 some standard instruments. The special theory, 

 however, showed that this statement is not merely 

 inconvenient as a working rule, but also 

 demonstrably false, for a bar must have different 

 measured lengths according as it is moving rela- 

 tive to the observer along or across the direc- 

 tion of its length. The possibility of a com- 

 parison was restored by Einstein's system of 

 light signals; time and length standards were 

 supposed unaltered by displacement, provided the 

 observer was moving with them. .But whether he 

 was moving with them or not, a certain interval 

 /ds, measured between consecutive vibrations 

 of the clock or between points on the bar, 

 remained unaltered. .\lso the condition that 

 yds was stationary for small variations in the 

 path was found to give the conditions satisfied by 

 a particle moving at a great distance from matter. 



Thus this differential element ds had a dual 

 importance in the special relativity theory. In the 

 general theory this is generalised, but it may be 

 noticed that it is just possible that the two roJex 

 may really be separated in a gravitational field. 

 The consequences of this would be peculiar. It 

 is well known that the assumption that {/s. 

 taken through a period of vibration of an atom, is 

 independent of position, leads to the prediction of 

 a shift of solar spectral lines; though this is so 

 mixed up with shifts arising from other causes 



