L E C T U R E A T K E I O U N I V E R S I T Y 8 5 5 “The Theory of Relativity is a theory of principle. To understand it, the principles on which it rests must be grasped. But, before stating these, it is necessary to point out that the theory of relativity has two sets of principles, which each seem to have their own special laws: the special relativity theory and the general theory of relativity. What Is Motion? “For some time, it has been well known that, in describing the motion of a body, we must refer to another body. The motion of a car is described with reference to the ground, of a planet, with reference to the total assemblage of visible fixed stars. In physics, the bodies, to which motions are specially referred, are termed systems of coordinates. The laws of me- chanics of Galileo and Newton can be formulated only by using a system of coordinates. “The state of motion of a system of coordinates cannot be chosen arbitrarily, if the laws of mechanics are to hold good (it must be free from twisting and from acceleration). The system of coordinates employed in mechanics is called an inertia-system. So far as mechan- ics are concerned, the state of motion of an inertia-system is not restricted by nature to one condition. The condition in the following proposition suffices: a system of coordinates moving in the same direction and at the same rate as a system of inertia is itself a system of inertia. The special relativity theory is, therefore, the application of the following proposi- tion to any natural process:— The Fundamental Law “‘Every law of nature which holds good with respect to a coordinate system K must also hold good for any other system L, provided that K and L are in uniform movement of trans- lation.’ “The second principle, on which the special relativity theory rests, is that on the constan- cy of the velocity of light in a vacuum. Light in a vacuum has a definite and constant veloc- ity, independent of the velocity of its source. This is already contained in the Maxwell- Lorentz theory of electro-dynamics. “The two principles mentioned have received strong experimental confirmation but do not seem to be logically compatible. The special relativity theory achieved their logical rec- onciliation by making a change in kinematics, that is to say, in the doctrine of the physical laws of space and time. It became evident that a statement of the coincidence of two events could have a meaning only in connection with a system of coordinates, that the mass of bod- ies and the rate of movement of clocks must depend on their state of motion with respect to the coordinates. “But the older physics including the laws of motion of Galileo and Newton, clashed with the relativistic kinematics indicated. The latter gave origin to certain generalized mathemat- ical conditions, with which the laws of nature would have to conform, if the two fundamen- tal principles were compatible. Physics had to be modified. The most notable change was a new law of motion for (very rapidly) moving mass points, and this soon came to be veri- fied in the case of electrically-laden particles. The most important result of the special rel- ativity system concerned the inert mass of a material system. It became evident that the inertia of such a system must depend on its energy content, so that we were driven to the