ABSTRACT
One of the most difficult matters in all controversy is to distinguish disputes about words from disputes about facts: it ought not to be difficult, but in practice it is. This is quite as true in physics as in other subjects. In the seventeenth century there was a terrific debate as to what ‘force’ is; to us now, it was obviously a debate as to how the word ‘force’ should be defined, but at the time it was thought to be much more. One of the purposes of the method of tensors, which is employed in the mathematics of relativity, is to eliminate what is purely verbal (in an extended sense) in physical laws. It is of course obvious that what depends on the choice of co-ordinates is ‘verbal’ in the sense concerned. A person punting walks along the boat, but keeps a constant position with reference to the river-bed so long as she or he does not pick up the pole. The Lilliputians might debate endlessly whether the punter is walking or standing still; the debate would be as to words, not as to facts. If we choose co-ordinates fixed relatively to the boat, the punter is walking; if
we choose co-ordinates fixed relatively to the river-bed, the punter is standing still. We want to express physical laws in such a way that it shall be obvious when we are expressing the same law by reference to two different systems of co-ordinates, so that we shall not be misled into supposing we have different laws when we only have one law in different words. This may be accomplished by the method of tensors. Some laws which seem plausible in one language cannot be translated into another; these are impossible as laws of nature. The laws that can be translated into any co-ordinate language have certain characteristics: this is a substantial help in looking for such laws of nature as the theory of relativity can admit to be possible. Of the possible laws, we choose the simplest one which predicts the actual motion of bodies correctly: logic and experience combine in equal proportions in obtaining this expression.
