Arthur Eddington

“ One of the most important consequences of the relativity theory is the unification of inertia and gravitation.
The beginner in mechanics does not accept Newton's first law of motion without a feeling of hesitation. He readily agrees that a body at rest will remain at rest unless something causes it to move; but he is not satisfied that a body in motion will remain in uniform motion so long as it is not interfered with. It is quite natural to think that motion is an impulse which will exhaust itself, and that the body will finally come to a stop. ”

“ The amount of energy or mass in a given region is always a definite quantity; but the amount attributable to a particle is only definite when the motion is uniform. In rigorous work it is generally necessary to consider the mass not of a particle but of a region.
The motion of matter from one place to another causes an alteration of the gravitational field in the surrounding space. If the motion is uniform, the field is simply convected; but if the motion is accelerated, something of the nature of a gravitational wave is propagated outwards. ”

“ Thus in the theory of relativity momentum appears as an invariant mass multiplied by a modified velocity . The physicist, however, prefers for practical purposes to keep to the old definition of momentum as mass multiplied by the velocity . We have , accordingly the momentum is separated into two factors, the velocity , and a mass , which is no longer an invariant for the particle but depends on its motion relative to the observer's space and time. ”

“ The increase of mass with velocity simply means that the energy of motion has been added on. We are emboldened to do this because in the case of an electrical charge the electrical mass is simply the energy of the static field. Similarly the mass of light is simply the electromagnetic energy of the light.
In our ordinary units the velocity of light is not unity, and a rather artificial distinction between mass and energy is introduced. They are measured by different units, and energy has a mass where is the velocity of light in the units used. ”

“ So long as forces are confined to the thrusts and tensions of elementary mechanics, where there is supposed to be direct contact of material, there is good ground for this distinction; we can visualise the active hammering of the molecules on the body, causing it to change its motion. But when force is extended to include the gravitational field the distinction is not so clear.
For our part we deny the distinction in this last case. Gravitational force is not an active agent working against the passive tendency of inertia. Gravitation and inertia are one. ”

“ Now at each successive instant a particle is displaced continuously in time if not in space; and so in our four-dimensional representation which gives a bird s-eye-view of all time, the pucker has the form of a long groove along the track of the particle. Now such a groove or pleat in a continuum cannot take an arbitrary course—as every dress-maker knows. Einstein's law of gravitation gives the rule according to which the curvatures at any point of space-time link on to those at surrounding points; so that when a groove is started in any direction the rest of its course can be forecasted. ”

“ After mass and energy there is one physical quantity which plays a very fundamental part in modern physics, known as Action. Action here is a very technical term, and is not to be confused with Newton's "Action and Reaction." In the relativity theory in particular this seems in many respects to be the most fundamental thing of all. The reason is not difficult to see. If we wish to speak of the continuous matter present at any particular point of space and time, we must use the term density. ”

“ The uniform straight track is only relative to some mesh-system, which is assigned by arbitrary convention. We cannot imagine that a body looks round to see who is observing it and then feels an innate tendency to move in that observer's straight line—probably at the same time feeling an active force compelling it to move some other way. If there is anything that can be called an innate tendency it is the tendency to follow what we have called the natural track—the longest track between two points. ”

“ We might restate the first law of motion in the form "Every body tends to move in the track in which it actually does move, except in so far as it is compelled by material impacts to follow some other track than that in which it would otherwise move." ”

“ Wherever there is matter [3] there is action and therefore curvature; and it is interesting to notice that in ordinary matter the curvature of the space-time world is by no means insignificant. For example, in water of ordinary density the curvature is the same as that of space in the form of a sphere of radius 570,000,000 kilometres. The result is even more surprising if expressed in time units ”

“ 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. ”

“ When continuous matter is admitted, any kind of space-time becomes possible. The law of gravitation instead of denying the possibility of certain kinds, states what values of , i.e. what distribution and motion of continuous matter in the region, are a necessary accompaniment. ”

“ 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. ”