146 GRAVITATION—THE EXPLANATION 



of only one set of ten coefficients and complete uniform- 

 ity of the other ten. It therefore does not leave us with- 

 out the basis of uniformity of which Whitehead in his 

 own way perceived the necessity. Moreover, this uni- 

 formity is not the result of a law casually imposed on the 

 world; it is inseparable from the conception of survey of 

 the world from within — which is, I think, just the con- 

 dition that Whitehead would demand. If the world of 

 space-time had been of two or of three dimensions 

 Whitehead would have been entirely right; but then 

 there could have been no Einstein theory of gravitation 

 for him to criticise. Space-time being four-dimensional, 

 we must conclude that Whitehead discovered an im- 

 portant truth about uniformity but misapplied it. 



The conclusion that the extension of an object in any 

 direction in the four-dimensional world is determined by 

 comparison with the radius of curvature in that direction 

 has one curious consequence. So long as the direction 

 in the four-dimensional world is space-like, no difficulty 

 arises. But when we pass over to time-like directions 

 (within the cone of absolute past or future) the directed 

 radius is an imaginary length. Unless the object 

 ignores the warning symbol V — i it has no standard 

 of reference for settling its time extension. It has no 

 standard duration. An electron decides how large it 

 ought to be by measuring itself against the radius of 

 the world in its space-directions. It cannot decide how 

 long it ought to exist because there is no real radius of 

 the world in its time-direction. Therefore it just goes on 

 existing indefinitely. This is not intended to be a rigor- 

 ous proof of the immortality of the electron — subject 

 always to the condition imposed throughout these 

 arguments that no agency other than metric interferes 

 with the extension. But it shows that the electron 



