8io 



NATURE 



[February 17, 1921 



cause, and the principle of relativity in its two 

 phases, special relativity (the restricted theory) 

 and general relativity, is essentially concerned 

 with these two concepts. The first phase, in its 

 negativity towards the aether hypothesis, is a re- 

 form of the notion of substance ; and the second, 

 in its rejection of influence and its substitution of 

 equivalence for attraction in a new theory of 

 gravitation, is a reform of the notion of cause. 



Two opposing principles in regard to both these 

 concepts — substance and cause — have been strug- 

 gling to establish themselves throughout the 

 modern period — one taking as its type the ob- 

 jective or passive aspect presented by the world 

 to the mind of the observer, the other taking as 

 its type the subjective activity of the mind itself 

 in perceiving, imagining, understanding, willing, 

 and acting. The first type we have in Descartes' 

 concept of material substance as consisting in ex- 

 tension alone, and in his concept of cause as the 

 mechanical action and interaction of a definite 

 quantity of movement imparted to the extended 

 substance — the concept of a mechanism which em- 

 braces the whole universe, organised and unorgan- 

 ised, exclusive only of the other substance, 

 thought or thinking, present in human beings 

 alone. Later we have the same type in the more 

 familiar concepts of Newton — absolute time and 

 absolute space. "Absolute time, in itself, and 

 from its own nature, flows equally, without rela- 

 tion to anything external." "Absolute space, in 

 its own nature, without relation to anything ex- 

 ternal, remains always similar and unmovable." 

 The other type of concept we have in Leibniz's 

 monadology. Substance is not passive, but active ; 

 cause is not movement, but force. What does 

 nothing is nothing. Time and space are ordines 

 rerum non res. Things are centres of active 

 force. 



It is with these concepts of substance and cause 

 that the principle of relativity is primarily and 

 mainly concerned, and these concepts are meta- 

 phvsical constructions. Experimental facts have 

 called for the formulation of the principle, but 

 those facts themselves have slight importance in 

 the practical sphere ; it is their theoretical con- 

 sequences which are far-reaching and revolution- 

 ary. They are facts which prove to be decisive 

 in regard to metaphysical problems. The experi- 

 ments are concerned with such infinitesimals as 

 forty-t\yo seconds in relation to a century, or a 

 variability of 2J in. in the diameter of the earth. 

 It is not the facts themselves, therefore, that are 

 important, but their significance. According to 

 the view which I have put forward in my book, 

 "The General Principle of Relativity in its Philo- 

 sophical and Historical Aspect " (Macmillan and 

 Co.), the principle of relativity definitely decides 

 for us that our universe is monadic, and that our 

 science does not derive its validity from a reality 

 independent of the monads, but from a power in- 

 herent in the monads to co-ordinate ever-varying 

 points of view. By monads I mean minds, but 

 minds conceived as metaphysical reals. 



The point of supreme and central importance 

 NO. 2677, VOL. 106] 



in the principle of relativity in its bearing 

 on metaphysics is its negative attitude to the con- 

 cept of absolute space and absolute time con- 

 tinua. The principle accepts the null result of 

 the experiments as decisive in regard to the non- 

 reality in the physical sense of such continua, and 

 it refuses to recognise any necessity to construct 

 ad hoc a hypothetical absolute space-time system. 

 On the other hand, it claims to provide a formula 

 which expresses the identity ef an event for two 

 observers in different systems who pronounce it 

 to be one and the same, without the necessity of 

 affirming an absolute order independent of their 

 systems of reference. 



Why does this seem paradoxical and in contra- 

 diction to our ordinary experience? Because our 

 experience consists in the observation of events 

 which we do not cause ; which we refer to in our 

 intercourse with our fellows as common to them 

 and to us ; and to which throughout life we, auto- 

 matically or consciously, react. We argue by 

 what appears to us the most perfectly natural 

 reasoning that the identity of an event for two 

 different observers implies an absolute order by 

 reference to which alone differences of observa- 

 tion can be reconciled. This absolute order, we 

 think, can be nothing else but the determination 

 of every event in regard to every other event in an 

 absolute coexistence in space and in an absolute 

 succession in time. We conceive, therefore, an 

 absolute space-time order, and suppose our private 

 space-time systems are related to it. Such is the 

 course of reasoning which appears natural, and 

 such is the logical necessity from which it appears 

 impossible to escape. Metaphysicians have long 

 disputed it, but their arguments have been gener- 

 ally set aside as logomachies. Experiment has 

 now falsified it. 



What sort of thing, then, is the relativist uni- 

 verse? Substance and cause — that is, the prin- 

 ciple of unity and the principle of uniformity — are 

 definitely transferred from the object to the sub- 

 ject of experience. I do not mean that object and 

 subject are dissociated ; I mean that substance 

 and cause are declared to be functions of the 

 essential activity, and not of the passivity of ex- 

 perience. Thus the universe depends on the 

 subject of experience, not, indeed, in the old and 

 often derided sense in which the philosopher is 

 caricatured as evolving an external world out of 

 his own inner consciousness, as the spider spins 

 its web, but in the sense that the universe is the 

 co-ordination which the observer effects. The 

 universe has four dimensions — the three dimen- 

 sions of space, and the one dimension of time. 

 The principle of co-ordination is that every ob- 

 server uses his own axes of dimension, taking his 

 system of reference as fixed in relation to all J 

 systems which for him are moving, and he is | 

 able to do so because his four axes are variable, 

 and every change in his own system of reference, 

 relatively to other systems, is compensated by a 

 variation in his axes of co-ordination which pre- 

 serves the ratio constant. 



The universe, then, which the principle of rela- 



