Page:Eddington A. Space Time and Gravitation. 1920.djvu/82

66 fields of force, we must return to the four-dimensional world of space-time. The observer is progressing along a certain track in this world. Now his course need not necessarily be straight. It must be remembered that straight in the four-dimensional world means something more than straight in space; it implies also uniform velocity, since the velocity determines the inclination of the track to the time-axis.

The observer in the accelerated lift travels upwards in a straight line, say 1 foot in the first second, 4 feet in two seconds, 9 feet in three seconds, and so on. If we plot these points as $$x$$ and $$t$$ on a diagram we obtain a curved track. Presently the speed of the lift becomes uniform and the track in the diagram becomes straight. So long as the track is curved (accelerated motion) a field of force is perceived; it disappears when the track becomes straight (uniform motion).

Again the observer on the earth is carried round in a circle once a day by the earth's rotation; allowing for steady progress through time, the track in four dimensions is a spiral. For an observer at the north pole the track is straight, and there the centrifugal force is zero.

Clearly the artificial field of force is associated with curvature of track, and we can lay down the following rule:—

Whenever the observer's track through the four-dimensional world is curved he perceives an artificial field of force.

The field of force is not only perceived by the observer in his sensations, but reveals itself in his physical measures. It should be understood, however, that the curvature of track must not have been otherwise allowed for. Naturally if the observer in the lift recognises that his measures are affected by his own acceleration and applies the appropriate corrections, the artificial force will be removed by the process. It only exists if he is unaware of, or does not choose to consider, his acceleration.

The centrifugal force is often called "unreal." From the point of view of an observer who does not rotate with the earth, there is no centrifugal force; it only arises for the terrestrial observer who is too lazy to make other allowance for the effects of the earth's rotation. It is commonly thought that this "unreality" quite differentiates it from a "real" force like gravity; but if we try to find the grounds of this distinction they evade us.