Page:Eddington A. Space Time and Gravitation. 1920.djvu/163

IX] that time that the kinetic energy, which forms part of the mass, is being passed on to another particle or radiated into the surrounding field; and it is scarcely possible to define the moment at which this energy ceases to be associated with the particle and must be reckoned as broken loose. 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. The velocity of propagation is the velocity of light. The exact laws are not very simple because we have seen that the gravitational field modifies the velocity of light; and so the disturbance itself modifies the velocity with which it is propagated. In the same way the exact laws of propagation of sound are highly complicated, because the disturbance of the air by sound modifies the speed with which it is propagated. But the approximate laws of propagation of gravitation are quite simple and are the same as those of electromagnetic disturbances.

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. Density multiplied by volume in space gives us mass or, what appears to be the same thing, energy. But from our space-time point of view, a far more important thing is density multiplied by a four-dimensional volume of space and time; this is action. The multiplication by three dimensions gives mass or energy; and the fourth multiplication gives mass or energy multiplied by time. Action is thus mass multiplied by time, or energy multiplied by time, and is more fundamental than either. Rh