MATTER, SPACE, AND TIME 257 



though temporary increase of weight ; indeed, a 

 mass hung from a spring balance would weigh 

 heavier till the upward speed of the lift became 

 uniform. Einstein assumed that this principle 

 of equivalence held not only for mechanical but 

 also for electrical effects, including light. 



The application of these ideas involved great 

 mathematical difficulties, and Einstein did not 

 publish a full account of his researches till 191 5. 

 It then appeared that many of the theories of 

 the older physics, including Newton's law of 

 gravitation, might be replaced by new explana- 

 tions of the phenomena. 



Mathematical analysis shows that the space 

 and space-time of Einstein and Minkowski have 

 certain peculiarities. At places they are impene- 

 trable, and there we may fairly suppose to exist 

 what we call particles of matter. Near these 

 places the equations show that space and space- 

 time are subject to what in a line or a surface we 

 call curvature. How three dimensional space and 

 four dimensional space-time can be curved, we must 

 imagine as best we may. The wonders of nature 

 are not necessarily comprehensible to our minds. 



The curvature of space and space-time may 

 perhaps best be left in the decent obscurity of 

 mathematical equations. The equations show 

 that the natural path of a particle of matter 

 traversing a region near a massive body is not 

 the straight line passed over with uniform speed 

 contemplated by Newton's First Law of Motion, 

 but a path in space-time that bends towards the 

 mass in space, and in time moves faster the nearer 

 it passes to the matter — the path, in fact, of a 

 planet swinging round the sun. 



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