apparently uncaused field of force. But is there no debt to pay, even when the inertial frame is used? In that case there is no gravitational or centrifugal force at infinity; but there is still inertia, which is of the same nature. The distinction between force as requiring a cause and inertia as requiring no cause cannot be sustained. We shall not become any more solvent by commuting our debt into pure inertia. The debt is inevitable whatever mesh-system is used; we are only allowed to choose the form it shall take.
The debt after all is a very harmless one. At infinity we have the absolute geodesics in space-time, and we have our own arbitrarily drawn mesh-system. The relation of the geodesics to the mesh-system decides whether our axes shall be termed rotating or non-rotating; and ideally it is this relation that is determined when a so-called absolute rotation is measured. No one could reasonably expect that there would be no determinable relation. On the other hand uniform translation does not affect the relation of the geodesics to the mesh-system—if they were straight lines originally, they remain straight lines—thus uniform translation cannot be measured except relative to matter.
We have been supposing that the conditions found in the remotest parts of space accessible to observation can be extrapolated to infinity; and that there are still definite natural tracks in space-time far beyond the influence of matter. Feelings of objection to this view arise in certain minds. It is urged that as matter influences the course of geodesics it may well be responsible for them altogether; so that a region outside the field of action of matter could have no geodesics, and consequently no intervals. All the potentials would then necessarily be zero. Various modified forms of this objection arise; but the main feeling seems to be that it is unsatisfactory to have certain conditions prevailing in the world, which can be traced away to infinity and so have, as it were, their source at infinity; and there is a desire to find some explanation of the inertial frame as built up through conditions at a finite distance.
Now if all intervals vanished space-time would shrink to a point. Then there would be no space, no time, no inertia, no anything. Thus a cause which creates intervals and geodesics
