Page:Eddington A. Space Time and Gravitation. 1920.djvu/84

68 is some super-observer. If he feels a field of force, then that force really exists. Lesser beings, such as the occupants of the falling projectile, have other ideas, but they are the victims of illusion. It is to this super-observer that the mathematician appeals when he starts a dynamical investigation with the words "Take unaccelerated rectangular axes, $$O_x$$, $$O_y$$, $$O_z$$…." Unaccelerated rectangular axes are the measuring-appliances of the super-observer.

It is quite possible that there might be a super-observer, whose views have a natural right to be regarded as the truest, or at least the simplest. A society of learned fishes would probably agree that phenomena were best described from the point of view of a fish at rest in the ocean. But relativity mechanics finds that there is no evidence that the circumstances of any observer can be such as to make his views preeminent. All are on an equality. Consider an observer $$A$$ in a projectile falling freely to the earth, and an observer $$B$$ in space out of range of any gravitational attraction. Neither $$A$$ nor $$B$$ feel any field of force in their neighbourhood. Yet in Newtonian mechanics an artificial distinction is drawn between their circumstances; $$B$$ is in no field of force at all, but $$A$$ is really in a field of force, only its effects are neutralised by his acceleration. But what is this acceleration of $$A$$? Primarily it is an acceleration relative to the earth ; but then that can equally well be described as an acceleration of the earth relative to $$A$$, and it is not fair to regard it as something located with $$A$$. Its importance in Newtonian philosophy is that it is an acceleration relative to what we have called the super-observer. This potentate has drawn planes and lines partitioning space, as space appears to him. I fear that the time has come for his abdication.

Suppose the whole system of the stars were falling freely under the uniform gravitation of some vast external mass, like a drop of rain falling to the ground. Would this make any difference to phenomena? None at all. There would be a gravitational field; but the consequent acceleration of the observer and his landmarks would produce a field of force annulling it. Who then shall say what is absolute acceleration?

We shall accordingly give up the attempt to separate artificial fields of force and natural gravitational fields; and call the whole