Although we may be repeating ourselves unnecessarily, we cannot help but feel that the easiest way for the layman to grasp these difficult concepts will be to return to the well-known illustration of the relativity of a visual angle. When we perceive an object, say a telegraph pole, we see it under a certain angle, which we may call the visual angle. Is this visual angle real? Of course it is; we can measure it and define it physically as the angle subtended by two Euclidean straight lines extending between our eye and the two extremities of the pole. It is real but it expresses a relationship—a relationship between the positions of the observer and pole. It is certainly not inherent in the pole, since as the observer changes his position the visual angle changes in magnitude, though nothing happens to the pole in the meantime.
Visual angle in classical science is analogous to distance in Einstein’s theory. Our rod has no true length any more than the telegraph pole has any true visual angle. The whole significance of relativity is precisely to deprive length and duration of the absolute characteristics which classical science attributed to them. In short, when we are asked whether the rod has really been contracted and lost part of its length, we might counter by asking whether the telegraph pole has really been modified and lost part of its visual angle. Just as, if we omit to stipulate the position of the observer, the visual angle of the pole has no meaning and can teach us nothing about the pole, so now, in relativity, the length of the rod has no meaning in itself and can teach us nothing about the rod.
All these arguments developed on the score of length apply in similar fashion to duration. Both length and duration are relatives having no absolute significance in the universe.
The critic will generally balk at these statements and be inclined to say: “What nonsense! The length of the rod is immanent in the rod and can in no wise be affected by the observer’s motion or by the frame’s existence. The observer might die, the frame might disappear; what has all this to do with the length of the concrete entity we call the rod? The length of the rod may appear longer or shorter according to its relative motion; but we must not confuse appearance and reality. Thus, a man standing 100 yards away appears to us shorter than when he is close up, but it would never enter our minds to say that he was really reduced in stature. Just as the height of the man is independent of our position and of our existence as observers, so is the length of the rod independent of our relative velocity.”
Now we might readily concede to the critic the right to maintain that the existence and absolute characteristics of the rod are in no wise dependent on the motion or the existence of an observer. But the critic is begging the question when he assumes without further ado that these absolute characteristics are expressed by the length of the rod. This length enters into existence only when a definite space is specified; till then it is meaningless. And in the absence of an observer there is no such thing as a space, but merely four-dimensional space-time. The absolute characteristics of the rod thus refer to space-time, and this eliminates all primary qualities such as length. The situation is of course not easy to grasp at first blush and is still less easy to explain, but in view of the extreme importance of the matter we shall do our best to clarify it by slightly varying the presentation.
Let us first examine the problem from the standpoint of classical science. Consider an observer who walks away from a point
on the surface of the earth. He finally comes to a stop after having walked a distance
from the point