8oo 



NATURE 



[February 17, 1921 



tivists have not dived down into the aether, as 

 someone must ultimately dive, and dissected out 

 the intrinsic speed of its turbulence— which is 

 really the fundamental velocity in existence^ — they 

 have utilised the more obvious and conspicuous 

 consequence of this fundamental speed, viz. the 

 uniform velocity with which the aether can convey 

 a great variety of signals. Indeed their attach- 

 ment to appliances like clocks and rods has led 

 them to pay almost undue reverence to the aether's 

 power of transmitting waves at a high and other- 

 wise unattainable speed. It is true that these 

 waves are among our methods of receiving and 

 conveying information ; but too much attention 

 may be paid to the mere reception of informa- 

 tion; and what is spoken of as "warping" is not 

 limited to space alone. For some philosophers 

 speak as if the duration of an event could be ex- 

 tended by merely delaying the reception of the 

 news of its end; as if we could prolong a man's 

 life by evading the tidings of his death, and might 

 be entitled to say, without absurdity, that a man 

 who died at seventy had lived seventy-one years 

 and a lot of miles, if we had travelled so far that 

 the messenger took a year to reach us. That such 

 things can be gravely uttered is surely a tribute to 

 the beauty and complexity of the mathematical 

 scheme which can temporarily so warp the judg- 

 ment even of the most competent. 



If I am wrong in this I share a fraction of rash- 

 ness with the admirable audacity of Einstein in 

 the Weltmacht oder Niedergang sort of atti- 

 tude which he takes up about his predicted shift 



of spectral lines. I feel a doubt whether those 

 lines will be found shifted — at least when the 

 observation is made outside a strong gravitational 

 field- — but I should be quite content either way, 

 and would not think of asking anyone to abandon 

 the method of relativity on that account.' 



For undoubtedly general relativity, not as a 

 philosophic theory but as a powerful and compre- 

 hensive method, is a remarkable achievement; and 

 an ordinary physicist is full of admiration for the 

 equations and the criteria, borrowed from hyper- 

 Geometers, applied by the genius of Einstein, and 

 expounded in this country with unexampled 

 thoroughness and clearness by Eddington. But, 

 notwithstanding any temptation to idolatry, a 

 physicist is bound in the long run to return to hrs 

 right mind ; he must cease to be influenced unduly 

 by superficial appearances, impracticable measure- 

 ments, geometrical devices, and weirdly ingenious 

 modes of expression ; and must remember that 

 his real aim and object is absolute truth, however 

 difficult of attainment that may be. that his func- 

 tion is to discover rather than to create, and that 

 beneath and above and around all Appearances 

 there exists a universe of full-bodied, concrete, 

 absolute, Reality. 



* Since the above paragraph was in type a Circular, dated January, 

 1921, ha^ reached me from Prof. Slipher, of the Lowell Observatory at 

 Flagstaff, Arizona, recording an extravagant rate of recession — something 

 like a thousand miles a second — for two specified nebula:, presumably of the 

 spiral class. But both nebula: are reported to have large and b'illiant 

 nuc ei ; and if the confentraiion of their aggregate ma<s were suflRctent — 

 that is, if their M/R or pt<2 were some two or three thousands of times 

 greater than that of our sun, and therefore of a totally different order from 

 that of oiir stellar system — the observation could be interpreted, not as 

 rccessicn, but as an Einstein shift of spec-ral lines. 



MODERN physics renders it probable that the 

 only fundamental forces in Nature are 

 those which have their origin in gravitation and 

 in the electromagnetic field. After the effects 

 proceeding from the electromagnetic field had been 

 co-ordinated by Faraday and Maxwell into laws 

 of striking simplicity and clearness, it became 

 necessary to attempt to explain gravitation also 

 on the basis of electromagnetism, or at least to 

 fit it into its proper place in the scheme of electro- 

 magnetic laws, in order to arrive at a unification 

 of ideas. This was actually done by H. A. 

 Lorentz, G. Mie, and others, although the success 

 of their work was not wholly convincing. At 

 the present time, however, in virtue of Einstein's 

 general theory of relativity, we understand in 

 principle the nature of gravitation, and the 

 problem is reversed. It is necessary to regard 

 electromagnetic phenomena, as well as gravita- 

 tion, as an outcome of the geometry of the 

 universe. I believe that this is possible when we 

 liberate the world-geometry (on which Einstein 

 based his theory) from an inherent inconsistency, 

 which is still associated with it as a consequence 

 of our previous Euclidean conceptions. 



NO. 2677, VOL. 106] 



Electricity and Gravitation 

 By Prof. H. Weyl. 



[Translated by Dr. Robert W. Lawson.] 



The great accomplishment of the theory of rela- 

 tivity was that it brought the obvious principle 

 of the relativity of motion into harmony with the 

 existence of inertial forces. The Galilean law of 

 inertia shows that there is a kind of obligatory 

 guidance in the universe, which constrains a body 

 left to itself to move with a perfectly definite 

 motion, once it has been set in motion in a par- 

 ticular direction in the world. The body does this 

 in virtue of a tendency of persistence, which 

 carries on this direction at each instant "parallel 

 to itself." At every position P in the universe, 

 this tendency of persistence (the " guiding field ") 

 thus determines the infinitesimal parallel displace- 

 ment of vectors from P to world-points indefinitely 

 near to P. Such a continuum, in which this idea 

 of infinitesimal parallel displacement is deter- 

 minate, I have designated as an "affinely x;on- 

 nected " one {affin zusammenhdngend). Accord- 

 ing to the ideas of Galileo and Newton, the 

 " aflfine connection " of the universe (the difference 

 between straight and curved) is given by its geo- 

 metrical structure. A vector at any position in 

 the universe determines directly and without 

 ambiguity, at every other position, and bv 



