382 



NA TURE 



[March 23, 1922 



hypothesis, and is of greater value as a guide to the selec- 

 tion of futureresearches. The recent developments of the 

 theory of relativity due to Profs. Weyl and Eddington 

 are of considerable importance as examples of the 

 value of increasing the range of a theory. Weyl has 

 generalised the geometry used by Einstein in order to 

 produce a function which can conveniently be made 

 to represent the electro-magnetic energy tensor ; and 

 Eddington, in accordance with the methodological 

 considerations mentioned above, has suggested still 

 more radical generahsations, with the view of pro- 

 ducing, if possible, some function which can be used 

 as an electronic energy tensor. By this we mean a 

 function which contains at least analogues of the main 

 properties of the electron. Towards this very im- 

 portant result Eddington has taken several significant 

 steps, though the physical aspect of this part of the 

 energy of a system, associated with the non-Maxwellian 

 forces, is by no means clear at present. It will ob- 

 viously be a matter of the greatest importance if it 

 proves possible to cover the electronic phenomena as. 

 well as the gravitational and electro-magnetic by a few 

 perfectly definite general assumptions of the same type 

 as those already introduced in relativity theory. 



Among the results obtained by Eddington, we may 

 direct attention to the fact that a natural unit of 

 action has made its appearance in terms of which both 

 the energy tensor and the electro-magnetic tensor can 

 be expressed. It appears that this unit of action is 

 10^1* times the quantum required in the quantum 

 theory, but the fact that the two energy tensors, 

 which so far have been treated on the lines of 

 world geometry, can be given in terms of the one 

 unit of action may well suggest further developments 

 which may accomplish ultimately the introduction of 

 a tensor to represent the electronic or non-Maxwellian 

 forces. 



But let us consider how these advances have been 

 brought about. On Weyl's theory, it is possible that 

 comparisons of length at different times and at different 

 places may yield discordant results according to the 

 route of comparison. In fact, a particular standard 

 of length should apparently be used only at the time 

 and place where it is, for in general, a vector will 

 change its value on describing a circuit. The funda- 

 mental apparatus required for measurement is there- 

 fore no longer, as in the days before relativity, a unit 

 standard, or indeed, a set of standards, one for each 

 point of space, but a set containing a unit for each 

 point of the fourfold manifold of space and time. 

 Such a system of measures, comprising a fourfold 

 series, is called a " gauge system " in Weyl's theory. 

 In this analytical scheme, however, zero length is 

 unique, and involves no specification of route. But 

 Eddington, with his idea that it may be possible to 

 introduce non-Maxwellian forces into the schema, 

 further generalises this theory by allowing that zero 

 length may not be unique. 



In allowing the generalised idea of measurement of 

 Weyl, and of course, still more in countenancing the 

 suggestion of Eddington, we are abandoning a well- 

 established belief in common sense ; and indeed, this 

 is the crux of the matter from the point of view of 

 ordinary life. But this is, of course, not the first time 

 that the theory of relativity has asked us to throw 



NO. 2734, VOL. 109] 



away the beliefs of everyday life. These theoretical 

 developments — and, in fact, the whole of relativity 

 theory — have attained so great a degree of complexity 

 that they have far outstripped the powers of deduction 

 possessed by naive common sense ; and this is so in 

 spite of the fact that they, in common with all other 

 branches of physics, started from ordinary common- 

 sense data. The difficulties, from a common-sense 

 point of view, of the theory of relativity, of which we 

 unfortunately hear so much, are due in great measure 

 to the fact that, owing to the extensive analytical 

 development, the postulates from which it starts have 

 no obvious connection with the physical facts which 

 the theory is designed to correlate. Tensors, for 

 example, involve quantities to which no simple physical 

 significance can at present be atft,ched. But even the 

 concept of energy, which has long since taken its 

 place as a physical idea, must at one stage of history 

 have been a difficult idea to the natural philosopher 

 previously limited to concepts such as force. The 

 con<;ept of action, as used in the quantum theory at 

 the present time, is scarcely one which the physicist, 

 left to himself, would readily employ, unless it is 

 regarded as being invariably an angular momentum. 

 The Lagrangian idea of generalised co-ordinates in 

 dynamics is another case of the same kind. The con- 

 cepts employed in relativity are at present remote 

 from physical ideas in exactly the same way, though 

 perhaps to a greater extent. 



The Theory of Relativity and Common Sense. 



In mathematical theories, not infrequently the logical 

 links between the premises of the problem and the 

 results deduced from them are so many in number 

 that no connection can at first sight be seen between 

 them. In fact, the greater the number of links the 

 more valuable the theory becomes. The purely mathe- 

 matical background of the theory of relativity consists 

 largely of developments which belong to highly special- 

 ised domains ; and it is not to be expected that 

 common sense can foresee the results obtainable from 

 specified assumptions which the data of common sense 

 have been found to require. Indeed, we might point 

 out that it is apparent from the mere fact that the 

 tensor theory has been built up into an extensive 

 branch of mathematics (which, of course, happened 

 long before its applications were dreamed of) that the 

 connection between the premises and the results is 

 too complicated to be dealt with without the aid of 

 a specially elaborated technique. It is therefore im- 

 politic to advance common-sense criticisms of the 

 various assumptions as to length which may pro- 

 visionally be advanced in the theory of relativity with 

 the definite object of effecting further comprehensive 

 correlations of physical facts. For common sense, 

 having provided the jumping-off ground, has a severely 

 restricted part to play in the more technical analysis 

 which the logical development of these assumptions 

 requires ; and it is at once the marvel and the allure 

 of the science of our day that mathematics, which is 

 but the child of common sense, has been able, owing 

 to the masterly researches carried on by the pioneers 

 of the nineteenth century, to transform the crude views 

 of her parents into the triumph of modern physics. 



