September 22, 1923] 



NA TURE 



427 



Paul, are standing together, and each marks the 

 hour O'' on his synchronous clock. Paul is then 

 carried suddenly outwards from the earth a specified 

 distance and back again in a rectilinear and uniform 

 movement relatively to the earth and at a velocity 

 of 259,807 kilometres a second. On his return, he 

 finds that Peter's clock records S"", while his, Paul's, 

 [records 4'', and it is proved by means of Lorentz's 

 [formulae that each clock has quite correctly measured 

 fthe time of one and the same event. 



Bergson's reply to his correspondent is clear and 

 tprecise, and involves no dispute as to actual matter 

 [of fact. He is able to admit the discrepancy in the 

 [time represented and also to affirm the identity of the 

 ■time lived, and yet to reconcile the paradox. He 

 [begins by pointing out that the shortening of the time 

 fas measured by Paul's clock is point to point analogous 

 to the contracting of Paul's dimensions as his distance 

 ^increases in Peter's perspective. Does Peter think, he 

 fasks, that because Paul diminishes in his perspective 

 'he is really becoming the dwarf he appears ? He does 

 [Dot, and he need not, and neither need he suppose 

 Ithat Paul's retarding clock is really registering shorter 

 fe'time. Paul's time, hke Paul's dimensions, is the time 

 \represented by Peter as that which belongs to a system 

 [of reference which is not Paul's, but Paul's-system-in- 

 [Uniform-translation-relatively-to-his-own. It is only 

 I Paul's system for Paul when he is immobilised in the 

 Fsystem. The paradox arises from supposing that 

 [Peter is immobilised in his system of reference, that 

 iPaul similarly is immobilised in his, and that the 

 Itwo systems, while immobilised, are moving relatively. 

 iThere is only one time lived, and that is the time of 

 [the system in which the observer is immobilised. This 

 ly be Peter or it may be Paul, but if it is Peter, 

 [Paul's time is represented time for Peter, and vice 

 \versa. Bergson's conclusion is : the formulae of 

 [Lorentz quite simply express what must be the measure- 

 lents attributed to the system S', if the physicist in 

 |system S is to imagine that the velocity of light is 

 the same for the physicist in S' a^ it is for him in S. 

 The second appendix deals with the reciprocity of 

 ccelerations. Is there perfect equivalence between 

 |relative systems of movement when, as in the shock 

 [experienced at the sudden stopping of a train, there 

 sis a psychical experience which has itself no equivalent ? 

 In other words, can there be pure reciprocity in accelera- 

 tions when certain of the phenomena concern only 

 one "'of the systems ? The argument of this appendix 

 is especially important, and illuminates for the first 

 time a very puzzling position. Stated briefly, it is 

 as follows. If we analyse the acceleration and fix its 

 elements as a succession of represented systems, each 

 in its turn being a system S' with represented time t' 

 NO. 2812, VOL. I 12] 



in relation to an immotDilised system S with real time 

 t, then the reciprocity is simple and complete; any 

 system which in relation to a system S is a system S' 

 can itself be a system S, provided that when S' changes 

 to S, t' becomes /. The symmetry is perfect. But 

 we, on the contrary, are continually representing to 

 ourselves one immobilised system S, to which we oppose 

 a multiplicity of distinct systems animated by various 

 movements, although we still represent them as one 

 unique system S'. When the passenger is thrown 

 from his seat by the sudden stoppage of the train, it 

 is because the material points of his body do not 

 preserve invariable positions in relation to the train. 

 There is no dissymmetry, but instead of a reciprocity 

 between S with t and S' with t' , we have to make the 

 real time belong successively to S" with t" , S'" with 

 t'", and so on. The complexity may be infinite, and 

 what we are trying to do is then to make one immobil- 

 ised system S reciprocal with infinite systems con- 

 sidered not as infinite but as one and unique. 



The most important appendix is the third : it deals 

 with real time and world-lines (" Temps propre et 

 ligne d'univers "). It is not possible to abbreviate 

 the argument, which must be read ; here we can only 

 indicate its nature. It takes its start from an equation 

 quoted in full from Jean Becquerel. Given a material 

 system of reference, all the points of which are in the 

 same state of movement (i.e. any portion of matter 

 in which the spatial distance separating events is null), 

 the time between two events which an observer will 

 measure is the time t proper to the system, the time 

 which its clocks are registering. A clock in a moving 

 system (whether moving uniformly or non-uniformly) 

 measures the length, divided by the velocity of light, 

 of the arc of the world-line of -the system. This 

 principle is worked out to show that in a system in 

 uniform translation (the earth, for example) two 

 clocks to be identical and s>Tichronous must be in 

 the same place. Let one be suddenly and rapidly 

 displaced, and at the end of a certain time (the time 

 of the system) be replaced, it will be found to be re- 

 tarded. Bergson accepts Becquerel's demonstration 

 (barely indicated here because the mathematical 

 equations are omitted), and proceeds to show how the 

 physicist and the philosopher have each a distinct 

 interest ; the physicist must represent a time which is 

 infinitely variable, the philosopher must affirm a 

 time which is absolute and lived. The two interests 

 must be respected and can be reconciled. 



Finally, Bergson considers Einstein's case of a field 

 of gravitation produced by the rotation of a disk. In 

 such a system, he quotes Einstein as saying, " It is 

 impossible to determine time by means of clocks 

 which are immobile as regards the system." But is 



