February 17, 192 1] 



NATURE 



«o3 



Evidently they are not giving us the tru% time- 

 interval ; and now that they are informed of the 

 discordance they ought to give up their out-of- 

 date procedure. But the astronomers reply : "Tell 

 us, then, how we ought to find this ' true time.' 

 By what characteristics are we to recognise it?" 

 No answer has been given. Michelson and others 

 sought in vain for an answer; for if our velocity 

 through the aether could be defined, it would single 

 out one universal system of time-measurement 

 which might reasonably (if somewhat arbitrarily) 

 be called true. Meanwhile the phrase true time 

 is a "meaningless noise." It is idle to contest 

 with those who hold that the thing exists 

 and ought to be regarded. "Who would give 

 a bird the lie, though he cry ' Cuckoo ' 

 never so? " 



The direction of Northampton measured by 

 astronomers at Cambridge is due west ; 

 measured by astronomers at Greenwich it is 

 north-west. It is no use to tell them that 

 they must adopt a different plan, and find 

 a " true direction " of Northampton which 

 does not show these discordances. They 

 reply : " VVe are perfectly aware that there must 

 be discordances, as you call them ; but that is 

 in the nature of a relative property like direction ; 

 as for this true direction which shall be the same 

 from all stations, we have no idea what you are 

 talking about." 



The time determined by astronomers and in 

 general use is thus a fictitious time, or, in the 

 usual phrase, it is relative to terrestrial observers. 

 Similarly it has been found that extension in 

 space is also relative. When the Copernican 

 theory led to the abandonment of the geocentric 

 view of the universe, the revolution did not go far 

 enough ; it was thought that we could pass to the 

 heliocentric outlook by merely allowing for what 

 in pure geometry would be called a change of 

 origin. Actually a more profound transformation 

 is necessary. For example, the Michelson-Morley 

 experiment is a terrestrial experiment, but its 

 theory is treated from a heliocentric point of view ; 

 that is to say, account is taken of the varying 

 orbital motion of the earth ; it furnishes a proof 

 of the famous FitzGerald contraction, and much 

 ingenuity has been spent on an electrical explana- 

 tion of this curious property of matter. Einstein's 

 theory waves this aside with the remark: "Of 

 course, your results appear strange when you 

 describe the apparatus in terms of a space and 

 time which do not belong to it. Your electro- 

 magnetic discussion is no doubt valid, but it i» 

 leading you away from the root of the matter ; the 

 immediate explanation lies in the difference 

 between the heliocentric and geocentric space and 

 time systems." 



Ft was shown by Minkowski that all these fic- 

 titious spaces and times can be united in a single 

 continuum of four dimensions. The question !s 

 often raised whether this four-dimensional sp.ice- 

 fimc is real, or merely a mathematical construc- 

 tion ; perhaps it is sufficient to reply that it can 

 at any rate not be less real than the fictitious space 

 NO. 2677, VOL. 106] 



and time which it supplants. Terrestrial ob- 

 servers divide the four-dimensional world into a 

 series of sections or thin sheets (representing 

 space) piled in an order which signifies time ; in 

 other w^ords, the enduring universe is analysed 

 into a succession of instantaneous states. But 

 this division is purely geometrical. The physical 

 structure of the enduring world is not laminated 

 in this way ; and there is nothing to prevent 

 another observer drawing his geometrical sections 

 in a different direction. In fact, he will do so if 

 his motion differs from ours. 



Now it may seem that we have been paying too 

 much deference to the astronomers: "After all, 

 they did not discover time. Time is something of 

 which we are immediately conscious." I venture 

 to differ and to suggest that (subject to certain 

 reservations) time as now understood itioj dis- 

 covered by an astronomer — Romer. By our sense 

 of vision it appears to us that we are present at 

 events far distant from us, so that they seem to 

 occur in instants of which we are immediately 

 conscious. Romer's discovery of the finite velo- 

 city of light has forced us to abandon that view ; 

 we still like to think of world-wide instants, but 

 the location of distant events among them is a 

 matter of hypothetical calculation, not of per- 

 ception. Since Romer, time has become a mathe- 

 matical construction devised to give the least dis- 

 turbance to the old illusion that the instants in our 

 consciousness are world-wide. 



Without using any external senses, we are con- 

 scious of the flight of time. This, however, is not 

 a succession of world-wide states, but a succession 

 of events at one place — not a pile of sheets, but 

 a chain of points. Common-sense demands that 

 this time-succession should be essentially different 

 from the space-succession of points along a line. 

 The preservation of a fundamental distinction be- 

 tween timelike succession and spacelike succession 

 is essential in any acceptable theory. Thus in the 

 four-dimensional world we recognise that there 

 are two types of ordered succession of events 

 which have no common measure ; type A is like 

 the succession of instants in our minds, and type B 

 is the relation of order along a line in space. 

 Proceeding from the instant "here-now," I can 

 divide the regions of the world into two zones, 

 according as they are reached by a succession of 

 type A (my absolute past and future), or of type 

 B (my absolute "elsewhere"). This scheme of 

 structure is very different from the supposed 

 laminated structure of the older view. Since we 

 believe that this distinction of types A and B 

 corresfKinds to something in the actual structure 

 of the world, it is likely to determine the various 

 natural phenomena that are observed. Thus it 

 determines the propagation of light, since it is 

 found thst the line of a light-pulse is alway* on 

 the boundary between the two zones above-men- 

 tioned. More important still, a particle of matter 

 is a structure which can occupy a chain of points 

 only of type A. Since we are limited by our 

 material bodies, it must be this type of succession 

 which we immediately experience ; we are aware 



