Page:Eddington A. Space Time and Gravitation. 1920.djvu/83

IV] The centrifugal force is made to disappear if we choose a suitable standard observer not rotating with the earth; the gravitational force was made to disappear when we chose as standard observer an occupant of Jules Verne's falling projectile. If the possibility of annulling a field of force by choosing a suitable standard observer is a test of unreality, then gravitation is equally unreal with centrifugal force.

It may be urged that we have not stated the case quite fairly. When we choose the non-rotating observer the centrifugal force disappears completely and everywhere. When we choose the occupant of the falling projectile, gravitation disappears in his immediate neighbourhood; but he would notice that, although unsupported objects round him experienced no acceleration relative to him, objects on the other side of the earth would fall towards him. So far from getting rid of the field of force, he has merely removed it from his own surroundings, and piled it up elsewhere. Thus gravitation is removable locally, but centrifugal force can be removed everywhere. The fallacy of this argument is that it speaks as though gravitation and centrifugal force were distinguishable experimentally. It presupposes the distinction that we are challenging. Looking simply at the resultant of gravitation and centrifugal force, which is all that can be observed, neither observer can get rid of the resultant force at all parts of space. Each has to be content with leaving a residuum. The non-rotating observer claims that he has got rid of all the unreal part, leaving a remainder (the usual gravitational field) which he regards as really existing. We see no justification for this claim, which might equally well be made by Jules Verne's observer.

It is not denied that the separation of centrifugal and gravitational force generally adopted has many advantages for mathematical calculation. If it were not so, it could not have endured so long. But it is a mathematical separation only, without physical basis; and it often happens that the separation of a mathematical expression into two terms of distinct nature, though useful for elementary work, becomes vitiated for more accurate work by the occurrence of minute cross-terms which have to be taken into account.

Newtonian mechanics proceeds on the supposition that there Rh