November 25, 1922] 



NA TURE 



697 



but now that shattering of nuclei is possible, and 

 now that rapid means of detection are feasible, there 

 is something to look for. The formation of strange 

 substances and unusual combinations may be expected, 

 and the composite nature even of the proton may yet 

 be demonstrated by the emission of something 

 fractional of extreme instability. Does not the 

 atomic bombardment of aluminium already yield 

 particles of extra long range ? 



I make no apology for this surmise. Speculation 

 as a temporary working hypothesis is sometimes 

 suggestive of further experiment, and that is its sole 

 justification. If the tendency of the discussion is 

 to uphold the greater simplicity of the extra-small 

 and extra-massive indivisible positive particle, well 

 and good ; but that would rather close the door on 

 one line of experiment, and it is not well to abandon 

 the mirror-image idea prematurely. The proton 

 may be an indivisible ultimate unit ; but that seems 

 unlikely, and we have learnt not to negative the 

 possibility of ascertainable structure lightly. It 

 seems barely credible, now, that it was as an indivisible 

 ultimate unit that we used to regard the atom ! 



The hypothesis that a proton is built up of positive 

 and negative but otherwise identical electrons may 

 yield a hydrogen nucleus too bulky for the facts, 

 and may otherwise have to be rejected, but the idea 

 at least leaves the door open to the extraordinarily 

 brilliant experimental physicists of to-day, and hence 

 as long as possible may be tentatively and provision- 

 ally encouraged. Oliver Lodge. 



Normanton, Lake, Salisbury. 



The Measurement of Intervals. 



I cannot resist Mr. Cunningham's invitation in 

 his review of my Romanes Lecture (Nature, Oct. 

 28, p. 568) to justify more precisely the transition 

 from the picture of world-history as a tangle of 

 world-lines to the scheme of intervals filling a con- 

 tinuum of space-time and demanding non-Euclidean 

 geometry. " Prof. Eddington seems to contemplate 

 as ' measurable ' the intervals between pairs of 

 points in this continuum which do not correspond 

 to events in the history of any particle or electron 

 in the material universe. But we wish to ask him 

 how these intervals are in practice to be measured." 

 Mr. Cunningham's point is that the picture which 

 we have to dissect is the actual history of the world, 

 and we are not allowed to alter it — to introduce 

 measurements which never were made, or to intro- 

 duce physically recognisable events at points where 

 nothing actually happened. I accept this limitation. 

 He admits, however, that all measurements that 

 have ever been made are contained in the picture, 

 and, I might add, all measurements that ever will 

 be made. Thus we have a large number of measured 

 intervals available for discussion ; and I think that 

 Mr. Cunningham, like myself, is convinced that the 

 geometry which these measured intervals obey is 

 not exactly Euclidean but is given correctly by 

 Einstein. When once this geometry is determined 

 we proceed to fill all space-time with calculated points 

 and intervals ; just as we ordinarily fill all space 

 with calculated points and distances after first 

 determining the geometry by means of a few distances 

 actually measured and a few points actually per- 

 ceptible. Only a small number of the calculated 

 points and intervals correspond to events and measure- 

 ments in the historical picture ; but whenever there 

 is a measured value it will agree with the calculated 

 value. 



As regards the status in physics of this scheme of 



NO. 2769, VOL. I IO] 



calculated points and intervals, it does not seem 

 necessary to make any hypothesis ; indeed, I scarcely 

 know what hypothesis could be made about it. At 

 the back of ray mind I vaguely suppose that it is 

 " closely descriptive " of an underlying relation- 

 structure of the actual world ; but whatever that 

 means (if it means anything) it is too indefinite to 

 use as an hypothesis. It is sufficient that we find 

 it profitable to talk about this scheme. But at 

 least its status is in no way inferior to the picture 

 of tangled world-lines which Mr. Cunningham finds 

 it convenient to start from. Material particles and 

 events outside us are not directly observed : they 

 are inferred from the fields (inertial and electro- 

 magnetic) which affect our bodies. But the field 

 itself is not directly observed ; it produces dis- 

 turbances in the bundle of world-lines called a man. 

 Inside the man the disturbance passes from field to 

 matter and matter to field in endless cycle. Who 

 shall say at what phase of the cycle it takes the 

 final plunge into the realm of consciousness and 

 actuality ? Rightly or wrongly the method of 

 science has always been to generalise from observa- 

 tion — to talk about a world which includes all that 

 has been observed and a great deal which has not 

 been observed. The astronomer does not make the 

 hypothesis that the moon exists when nobody is 

 observing it ; but he finds it profitable to talk about 

 a conceptual picture which contains a continuously 

 existing moon. The scheme of calculated' points 

 and intervals (aether, or field) or of tangled world- 

 lines (matter), or preferably both together, forms 

 the world which the physicist finds it profitable to 

 discuss ; he can scarcely attribute more virtue than 

 that to any world without wandering into meta- 

 physics. 



I must dissent entirely from Mr. Cunningham's 

 statement that " any geometrical system whatever 

 may be used for the purpose of attaching intervals." 

 Clearly if a wrong geometrical system is used, the 

 measured, intervals will expose it by their disagree- 

 ment. But Mr. Cunningham in this passage seems 

 to use the word interval as though it had no fixed 

 meaning and he could make it mean what he liked. 

 If I recollect rightly, I originally introduced the 

 name " interval," preferring it to the name " line- 

 element " then current, which seemed unsuitable 

 for a physical quantity as savouring too much of 

 pure mathematics. I intended " interval " to mean 

 a definite physical quantity — quite as definite as 

 " energy," for example ; and I desire to guard its 

 meaning jealously. If the meaning of " energy " 

 can be altered at pleasure, it is easy to upset the law 

 of conservation of energy ; and similarly by treating 

 " interval " and " length " as words meaning nothing 

 in particular, Mr. Cunningham has no difficulty in 

 disposing of my contention that the world is not a 

 Euclidean or flat world. 



It will be seen that Mr. Cunningham and I are 

 essentially in agreement that the merit of the Einstein 

 scheme of intervals is its simplicity — " profitable to 

 talk about " — rather than some kind of metaphysical 

 significance. He regards it as selected from many 

 other possible schemes because it gives a simple 

 representation of the motion of particles and light- 

 rays. That is a quite good enough reason for select- 

 ing it, but it must be borne in mind that it is not the 

 historical reason for choosing it. The fact that it 

 describes the exact motion of Mercury in a particu- 

 larly simple way was only discovered after the whole 

 scheme had been completed. The interest of Einstein's 

 scheme is that there is, not one reason, but several 

 reasons for selecting it. Not the least important 

 of these reasons is that the scheme expresses the 

 geometry of the world — in the sense in which the 



