practice, physics describes the relations of the events to our mesh-system; and all the terms of elementary physics and of daily life refer to this relative aspect of the world.
4. Quantities like length, duration, mass, force, etc. have no absolute significance; their values will depend on the mesh-system to which they are referred. When this fact is realised, the results of modern experiments relating to changes of length of rigid bodies are no longer paradoxical.
5. There is no fundamental mesh-system. In particular problems, and more particularly in restricted regions, it may be possible to choose a mesh-system which follows more or less closely the lines of absolute structure in the world, and so simplify the phenomena which are related to it. But the world-structure is not of a kind which can be traced in an exact way by mesh-systems, and in any large region the mesh-system drawn must be considered arbitrary. In any case the systems used in current physics are arbitrary.
6. The study of the absolute structure of the world is based on the "interval" between two events close together, which is an absolute attribute of the events independent of any mesh-system. A world-geometry is constructed by adopting the interval as the analogue of distance in ordinary geometry.
7. This world-geometry has a property unlike that of Euclidean geometry in that the interval between two real events may be real or imaginary. The necessity for a physical distinction, corresponding to the mathematical distinction between real and imaginary intervals, introduces us to the separation of the four-dimensional order into time and space. But this separation is not unique, and the separation commonly adopted depends on the observer's track through the four-dimensional world.
8. The geodesic, or track of maximum or minimum interval-length between two distant events, has an absolute significance. And since no other kind of track can be defined absolutely, it is concluded that the tracks of freely moving particles are geodesics.
9. In Euclidean geometry the geodesics are straight lines. It is evidently impossible to choose space and time-reckoning so that all free particles in the solar system move in straight lines.
