objects. Can one formulate in the mind the notion of length as apart from these material things which are measured; and, if so, how can such a notion of length be applied experimentally to the measurement of material things?
Questions of this nature we shall lay aside and shall return to the consideration of the length of material objects.
We have certain intuitive notions concerning the nature of matter which it is necessary for us to examine now. We have usually supposed that to revolve a steel bar, for instance, through an angle of ninety degrees has no effect upon its length. Let us suppose for the moment that this is not so; but that the bar is shorter when pointing in some directions than in others, so that its length is the product of two factors one of which is its length in a certain initial position and the other of which is a function of the direction in which the body points relative to that in the initial position. Suppose that at the same time all other objects experience precisely the same change for varying directions. It is obvious that in this case we should have no means of ascertaining this dependence of length upon the direction in which the body points.
To an observer placed in a situation like this it would be natural to assume that the length of the steel bar is the same in all directions. In other words, in arriving at his definition of length he would make certain conventions to suit his convenience.
Now suppose that the system of such an observer is set in motion with a uniform velocity v relative to the previous state of the system; and that at the same time all bodies on his system undergo simultaneously a continuous dilatation or contraction. This observer would have no means of ascertaining that fact; and accordingly he would suppose that his steel bar had the same length as before. In other words, he would unconsciously introduce a new convention concerning his measurement of length.
There is no a priori reason why our actual universe should not be such as the hypothetical one just described. To suppose it so unless our experience demands such a supposition would be unnatural; because it would introduce an unnecessary inconvenience. But suppose that in our growing knowledge of the universe there should come a time when we could more conveniently represent to ourselves the actual facts of our experience by supposing that all material things are subject to some such deformations as those which we have indicated above; there is certainly no a priori reason why we should not conclude that such is the essential nature of the structure of the universe.
Naturally we would not come to this conclusion without due consideration.
