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NATURE 



[August 26, 1920 



For it suggests really no more than the unification 

 of the observations of two sets of observers who 

 may be observing an absolute world in space-time, 

 by means of formulas of transformation in which 

 the observations of observers with one system of 

 co-ordinates can be rendered in terms of the co- 

 ordinates of observers with a different system. 'It 

 may be, he says, that the formulas are not really 

 independent, inasmuch as they are ultimately 

 numerical, and numbers may be wholly dependent 

 on an absolute space and time system. Thus it 

 would be an absolutely identical set of relations 

 which was observed from the two systems of 

 reference, moving rectilinearly with a relative velo- 

 city which remained uniform. 



But can this be accepted in the fresh light cast 

 by the general theory of relativity, of which the 

 special theory is now shown by Einstein to be a 

 mere special case? Here metaphysicians have to 

 look over a fence into ground at present mainly 

 occupied by the mathematician. But not exclu- 

 sively so occupied. The ground is in truth a 

 borderland where mathematics and epistemology 

 trench on each other, and the fence is not of 

 barbed wire. We are, indeed, compelled to try 

 to do the best we can with unfamiliar topics if we 

 would get at the truth about the nature of reality. 

 The relativity doctrine now extends to ac- 

 celerating motion. It has also, apparently, been 

 demonstrated that a principle of equivalence ob- 

 tains according to which any changes which an 

 observer takes to be due to what he supposes to 

 be attraction within a gravitational field would be 

 perceived by him in precisely the same way if 

 the observer's system of reference were moving 

 with the acceleration which was characteristic of 

 the gravitation at the observer's point of observa- 

 tion. The combination of these principles gives 

 us relativity of measurement in actual experience 

 without restriction. The gravitational principle 

 is, in addition, here based, not on a supposed 

 elementary law of gravitational force, whatever 

 that means, which would leave us in metaphysical 

 perplexities about action at a distance, but on 

 elementary laws of the motion of bodies relatively 

 to each other in a so-called gravitational field. 

 There is no decision either for or against 

 Euclidean geometry as a possible special case. 

 But there is a decision that space, as a physical 

 thing with unvarying geometrical properties, is 

 to be banished, just for the same sort of reasons 

 as the aether was banished before it. Only observ- 

 able things are to be recognised as real in the 

 new system of modern physicists. 



It is therefore asserted by Einstein that, all 

 motions and accelerations being relative to the 

 system of reference of the observer, neither space 

 NO. 2652, VOL. 105] 



nor time has physically independent objectivity. 

 They are not measurable in themselves. They 

 mean only the framework in which the minds of 

 the observers arrange physical events, according 

 to the conditions under which observation takes 

 place. We may choose such frameworks as we 

 please, but in point of fact we naturally choose 

 so that the application of our method is the one 

 that appears best adapted to the character of what 

 we observe. The standard used will give their 

 physical significances to our "geodetic lines." 

 The apparent order in space and time has no 

 independent existence. It manifests itself only in 

 the events that present themselves as so ordered. 



But the revolution in conception does not stop 

 here. As so-called "gravitational fields" are 

 everywhere present, the old special theory of rela- 

 tivity is nowhere an accurate account of pheno- 

 mena. The velocity of light, for instance, cannot 

 really be constant under all conditions. It is the 

 things we observe in space and time that give to 

 these their definite structure, and the relations in 

 them of the things depend on the system ot i '■ 

 servation. To get at the fundamental law of the 

 change which takes place in the space-time con- 

 tinuum we must look for the principle which 

 governs the motion of a point in it as of the form 

 of a differential law for the motion of such a 

 point, not merely in a straight line in the Euclid- 

 ean sense, but in a geodetic line which will be 

 relative to any possible form of motion and ac- 

 celeration in a gravitational field. If we can reach 

 such a differential law under the aspect of an 

 equation sufBciently elastic in its variables, we 

 shall be able to fit into it mathematical expressions 

 based on actual observation which give the "gravi- 

 tational potentials " required for the application 

 of the law. The form of the differential equation 

 which expresses the law must therefore be such 

 as to be applicable whatever may be the four co- 

 ordinates of reference of the observer of motion 

 in any conceivable gravitational field. The. prin- 

 ciple of equivalence necessitates this, and we get 

 as the result a science of motion depending on the 

 relativity of every kind of motion. All that is 

 required is that the co-ordinates which are the 

 variables in the equation of motion of a point- 

 mass moving uniformly and rectilinearly should 

 be so expressed as to be capable of transforma- 

 tion into the co-ordinates, whatever their shape, 

 of any system of reference which moves in any 

 path and has any accelerated motion whatsoever. 

 This appears to have been done completely. The 

 result is intelligible to the epistemologist who 

 can even do no more than look across the 

 boundary fence. The mathematical details and 

 scaffolding he may be wholly unable to appreciate. 



