ESSAYS 481 



Minkowski was the first who succeeded in finding a space-time framework which 

 would be the same for every observer, wherever and whenever he might be. He 

 showed that this would be the case for a system of four axes at right angles to one 

 another in a four-dimensional manifold representing space and time together, but 

 without distinguishing between them. He called this space-time, and showed that, 

 while it remained invariable, its resolution into space and time separately gave rise 

 to components which depended on the motion of the observer. It will be obvious 

 from what has gone before that space-time looked at from another point of view 

 would be identical with a four-dimensional space-manifold, so that the geometrical 

 treatment developed for dealing with the latter will be immediately applicable to 

 the former. 



The possibility now appears that this demonstrated variability of the space and 

 time framework of ordinary physics may be of such a nature as to nullify, by an 

 exact compensation, any and every evidence which we might otherwise hope to 

 obtain by experience of the contraction of material bodies in consequence of their 

 motion through the ether, just as no conceivable experiment could make a man 

 aware of an increase or decrease, however great, in his own size, if the whole scale 

 of nature simultaneously changed in the same proportion. The assumption, as a 

 working hypothesis, that this possibility may prove to be true, provides a perfectly 

 legitimate basis for a physical theory, and now forms the starting-point of what 

 physicists mean by the expression theory of relativity. 



The ultimate aim of all physical theory in the present stage of our knowledge 

 is the expression of phenomena in terms of strains set up in the ether and of the 

 stresses which give rise to them. The relativist's aim is, therefore, to show that a 

 more complete correlation of physical phenomena is obtainable in terms of stresses 

 and strains of the ether of the Minkowski time-space than in terms of the older 

 theory. Even, however, should the relativity theory reach a development realising 

 this expectation, we should, so far as we can see at present, have to translate our 

 results into terms of the older theory, or something corresponding to it, before we 

 could form physical conceptions of them — that is to say, before we could even think 

 intelligently about them except in so far as we could satisfy ourselves with mere 

 mathematical concepts. We should, however, expect to be able, by means of the 

 wider theory, to resolve some of the difficulties at present confronting us, and then 

 to revise the existing theory more or less completely, without transcending the 

 concepts of space and time to which our powers of visualisation are restricted. 



No physical theory that human intelligence is capable of constructing can ever 

 be more than a very imperfect model of natural phenomena. Should it prove 

 possible, and it appears probable that it may, mathematically to extend our 

 modelling beyond our powers of direct physical conception, we shall have to 

 apply a similar process to such models, modelling them in their turn, in order to 

 bring them within our limits of physical conception. 



Newton's mechanical world-models, and those of his immediate successors, 

 were imagined as built up of material particles of size apprehensible to our senses, 

 and any such system possesses the property of a mechanism — that the relations 

 between its constituent parts at any instant are determinable, provided our 

 mathematical methods are sufficiently powerful, from a knowledge of the relations 

 at an instant immediately preceding or succeeding it. That is to say, from a 

 complete determination of the system at any one instant we can deduce its state 

 at any past or future time. Newton's own mathematical methods, great as was 

 their advance on anything previously known, were adequate only to the solution of 

 comparatively simple problems. Lagrange extended them so far as to give a 



