8o^ 



NATURE 



[February 17, 192 1 



ofi the .jexistence of the other type only by 

 deductioa from the indications of our external 

 senses. 



Objection is sometimes raised to the extrava- 

 gantly important part taken by light-signals and 

 light-propagation in Einstein's discussion of space 

 and time. But Einstein did not invent a space 

 and time depending on light-signals ; he pointed 

 out that the space and time already in general 

 use depended on light-signals and equivalent pro- 

 cesses, and proceeded to show the consequences 

 of this. Turning from fictitious space and time 

 to the absolute four-dimensional world, we still 

 find the velocity of light playing a very prominent 

 part. It is scarcely necessary to offer any excuse 

 for this. Whether the substratum of phenomena 

 is called aether or world or space-time, one re- 

 quirement of its structure is that it should propa- 

 gate light with this velocity. 



The resolution of the four-dimensional con- 

 tinuum into a succession of instantaneous spaces 

 is not dictated by anything in the structure of the 

 continuum. Nevertheless, it is convenient, and 

 corresponds approximately to our practical out- 

 look on the world ; and it is rarely necessary to 

 go back to the undivided world. We have to go 

 back to the undivided world when a comparison is 

 made between the phenomena experienced by ob- 

 servers with different motions, who make the 

 resolution in different directions. Moreover, a 

 world-wide resolution into a space and time with 

 the familiar properties is possible only when the 

 continuum satisfies certain conditions. Are these 

 conditions rigorously satisfied? They are not; that 

 is Einstein's second great discovery. It is no more 

 possible to divide the universe in this way than 

 to divide the whole sky into squares. We have 



tried to make the division, and it has failed ; and 

 to cover up the consequences of the failure we 

 have introduced an almost supernatural agency — 

 gravitation. When we cease to strive after this 

 impossibility — a mode of division which there was 

 never any adequate reason for believing to be pos- 

 sible — gravitation as a separate agency becomes 

 unnecessary. Our concern here is with the bear- 

 ing of this result on time. Time is now not merely 

 relative, but local. The relative time for an ob- 

 server is a construction extended by astronomers 

 throughout the universe according to mathematical 

 rules ; but these rules break down in a region dis- 

 turbed by the proximity of heavy matter, and 

 cannot be fulfilled accurately. We can preserve 

 our time-partitions only by making up fresh rules 

 as we require them. The local time for a par- 

 ticular observer is always definite, and is the 

 physical representation of the flight of instants of 

 which he is immediately aware ; the extended mesh- 

 work of co-ordinates radiating from this is drawn 

 so as to conform roughly to certain rules — so as 

 not to violate too grossly certain requirements 

 which the untutored mind thought necessary at 

 one time. Subject to this, time is merely one of 

 four co-ordinates, and its exact definition is arbit- 

 rary. 



To sum up, world-wide time is a mathematical 

 system of location of events according to rules 

 which on examination can pnly be regarded as 

 arbitrary ; it has not any structural — and still less 

 any metaphysical — significance. Local time, which 

 for animate beings corresponds to the immediate 

 time-sense, is a type of linear succession of events 

 distinct from a pure spacelike succession ; and this 

 distinction is fully recognised in the relativity 

 theorv of the world. 



Theory and Experiment in Relativity.' 

 By Dr. Norman Campbell. 



SPACE" and "time" are the conceptions of 

 theory, not of laws. They are neither 

 necessary nor useful in the statement of the 

 results of any experiment. The experimental con- 

 cepts with which, like all theoretical ideas, they 

 are connected are such magnitudes as length, 

 area, volume, angle, period (of a system), or time- 

 interval. The numerical laws of experimental geo- 

 metry involve two or more " spatial " magnitudes 

 and no other magnitudes ; for example, the area of 

 a rectangle is proportional to the product of the 

 lengths of its sides. There are no laws relating 

 "temporal" magnitudes only. 



Relativity neither adds to nor subtracts from 

 the collection of spatial and temporal laws. The 

 laws which it explains all involve magnitudes that 

 are not spatial or temporal. And this is for- 

 tunate. For the subject has been so completely 



1 Since it is impossible to make a short article on a large suhjeft anything 

 but a summary, perhaps I may be permitted to re'^er sny reader who is 

 interested to my " Physics : The Elements " for a fuller discussion of many 

 of the questions raised. 



NO. 2677, VOL. 106] 



examined that it is very improbable that any 

 proposed new laws could be true. If relativity 

 predicted anything inconsistent with firmly estab- 

 lished experiment. Nature would not devote a 

 special number to discussing it. 



It may be objected that relativity does predict 

 new and strange laws ; it predicts that the velo- 

 city of light in a region remote from material 

 bodies is always the same ; and it predicts un- 

 familiar experiences of observers travelling rt 

 great speeds or in the neighbourhood of concen- 

 trated mass. But, it may be replied, the measure- 

 ment of the velocity of light does not involve only 

 spatial and temporal magnitudes ; we do not 

 measure that velocity as we do the velocity of a 

 material body ; an element of theory is always 

 involved. Again, we do not observe any disturb- 

 ance of geometrical laws in the neighbourhood of 

 the densest bodies we know. And as for Prof. 

 Eddington's observers in aeroplanes travelling 

 with half the velocity of light, no two human 



