SEMANTICS OF THE EINSTEIN THEORY 657
old language of 'matter', 'space', and 'time' was different from the structure of the outside world as we now know it. We found ourselves in a situation where we had to choose either to keep the old language which, as it differed from them in structure, could never give a coherent account of facts at hand, or else to build up a new language with structure similar to that of the outside world, in order to have the possibility of coherent conversation about it.
The invention of such a new language is of course an extremely difficult undertaking. In fact, it requires some genius to invent new, more structurally similar, forms of representation for the old facts. Lorentz, Einstein, and Minkowski prepared and finally produced such a structurally new language. The difficulty was that verbally we had already separated what empirically could not be separated. The problem was to amalgamate somehow the old structurally elementalistic language of 'space' and 'time' into a noh-elementalistic language. The key to such an amalgamation is found in the light-wave equation which gives us the structural information about the world,
This equation represents an equality. The left-hand side is expressed in 'spatial' terms onlythe distance between two points O and P. The right-hand side expresses the 'spatial' length, but in a 'temporal' term. We see that here we have means of translation, and a possibility of amalgamation of two elementalistic languages, which were not supposed to be intertranslatable.
The Lorentz-Einstein transformation formulae are
where v is the relative velocity of the two systems of coordinates, c, the constant velocity of light, and
The formulae forandwhich typify, on the left-hand side, x' a 'spatial' length anda 'time', are of particular interest. We see that on the right-hand side of the expressions the value of the 'spatial'is given by which
involves 'time'. The value of 'time',is given by, which involves
the 'spatial' length x. So we see that our amalgamation is complete, and separation impossible. The above formulae express structurally the simple experimental fact that 'space' and 'time' cannot be separated. At this point we are not ready to discuss 'matter'. This will be considered further on in this work (see Chapters XL and XLI).
The above formulae have also a very important physical and experimental meaning, as they introduce the 'contact' methods into our language. Our actual measurements of 'space' and 'time' are strictly connected with readings on some instruments, and involve therefore coincidences between pointers and 'simultaneity'. In all instances the finite velocity of propagation of signals must be taken into consideration. When our instrument, or the eye, is affected by signals there is always a delay due to the finite velocity of the propagation of the signals; These delays are part and parcel of our experiment, and so our formulae must contain terms explicitly involving this finite velocity of propagation. This innovation involves not only a most profound structural epistemo-logical and semantic revolution but supplies the very factor that enables us to formulate more structurally satisfactory languages (theories), which Lorentz, Einstein, and Minkowski have produced. 42