5°4 



NA TURE 



[October 14, 1922 



follows with the same logical necessity as in Zeno's 

 paradox that Achilles cannot overtake the tortoise. 



There is, however, a limitation even for the relativist 

 which, although it falls short of establishing an ab- 

 solute, is important to keep in mind. There is no 

 system of reference which a traveller can choose, by 

 entering which he might depart and return to find the 

 world younger, so that his journey would have been 

 backward in time. The reason is not the inconceiv- 

 ability of such a system, but the fact that it would 

 bring us into conflict with the law of causality. The 

 reversibility of causality which would require the 

 effect to come into existence before the cause, is un- 

 thinkable. Such then is the paradox. Relativity 

 requires that as we pass into a new system of reference 

 the relative movement of the new system shall be com- 

 pensated by changes in the spatio-temporal axes of 

 co-ordination in order to keep constant the velocity of 

 light. This means in the case supposed that two 

 years of the one system is the equivalent of two hundred 

 of the other. 



Bergson's solution of Einstein's paradox follows the 

 same line as his solution of the paradoxes of Zeno, but 

 the special application of his principle has a particular 

 interest. In the case of Zeno the essential point was 

 the insistence on the continuity, in the meaning of 

 absolute indivisibility, of true duration, the duration 

 which is lived and intuited, as distinct from the in- 

 finitely divisible continuity, mathematically defined, 

 of the schematised trajectory of the movement. The 

 mathematical time which we measure is really space. 

 In the case of Einstein's paradox Bergson argues that 

 the two systems, which are discordant as to their 

 simultaneity when taken as integral systems, must be 

 considered as continuously related, and this is possible 

 only so long as we do not abstract from the observer 

 who is attached to each. If, he says, we consider the 

 two observers in their different systems to be con- 

 tinuously in communication it is clear that each, while 

 regarding the other as a physicist co-ordinating a 

 system, will regard that co-ordinated system from the 

 standpoint of his own, and therefore, however different 

 the system may be, in so far as the two observers are 

 physicists and in so far as they are related observers, 

 the duration intuited is one and the same for both. But 

 here we shall ask, if the explanation is so simple, how 

 does the paradox arise ? Quite naturally, Bergson 

 replies, and this is the striking part of his argument, 

 because what the philosopher can do the physicist 

 cannot. The philosopher's concern is with reality 

 perceived or perceptible ; he, therefore, can never lose 

 sight of the interchangeability of the two systems. 

 He keeps them together by a kind of continual coming 

 and going between them. The physicist, on the other 

 NO. 2763, VOL. I ioj 



hand, whose only business is to co-ordinate the system 

 as a whole, must choose one and stand by his choice. 

 He cannot relate all the events of the universe to two 

 systems of different axes of co-ordination at one and 

 the same time. He must therefore regard the whole 

 system as concordant or discordant with the whole of 

 the other system, each taken as one and integral. For 

 the physicist is not concerned with time intuited but 

 only with time as a measurable dimension. 



We may see, then, how Einstein is able to affirm 

 that there are multiple times. We can place an 

 imaginary physicist at every point of space and his 

 time-system will necessarily be different from everv 

 other time-system; and our own time-system, so far 

 as we are physicists, has no privilege over the imaginary 

 time-systems. But, Bergson replies, into whichever 

 of these imaginary time-systems we project ourselves, 

 it becomes thereby time lived or intuited, and as we 

 can conceive ourselves to pass into any of them, there 

 is a real duration to which all the imaginary time- 

 systems belong. Thus is restored to us the unique 

 time, one and universal. 



Such is Bergson's solution. Does it dispose of the 

 problem ? The argument is certainly calculated to 

 reassure those who have been disturbed by the prin- 

 ciple of relativity, and to comfort those who are made 

 unhappy, rather than stimulated to activity, by 

 paradox. Yet there are many indications in his book 

 that Bergson himself does not feel he has said or is now 

 saying the last word. In the final remark, to which 

 we have already referred, he regards the generalised 

 theory as an extension of the argument of the restricted 

 theory with the difference that the emphasis is on 

 space rather than on time. He suggests that the 

 treatment of space on the same lines as those on which 

 he has dealt with time would show that the multiple 

 geometries are imaginary physicists' geometries ab- 

 stracted from their relation to and transformability 

 into the one and universal space-system which is the 

 intuition of the living individual. 



To a certain extent he is undoubtedly right, for we 

 may say truly that the restricted relativity is a case in 

 point of the generalised relativity. But there is a 

 problem which Bergson has left untouched while 

 giving indications that he is aware of it. This is the 

 relativity of magnitudes. Even Einstein has not, so 

 far, dealt with it specifically. Weyl, in his endeavour 

 to make the generalised theory include the whole 

 realm of electro-magnetic phenomena, has fore- 

 shadowed a relativity even more fundamental and 

 more universal than Einstein's, although so far he has 

 found no means, such as Einstein found, of submitting 

 the principle to experimental tests. In philosophy it 

 is of the deepest significance. Not only is there no 



