The measurement of time is effected by means of clocks. A clock is a thing which automatically passes in succession through a (practically) equal series of events (period). The number of periods (clock-time) elapsed serves as a measure of time. The meaning of this definition is at once clear if the event occurs in the immediate vicinity of the clock in space ; for all observers then observe the same clock-time simultaneously with the event (by means of the eye) independently of their position. Until the theory of relativity was propounded it was assumed that the conception of simultaneity had an absolute objective meaning also for events separated in space.
This assumption was demolished by the discovery of the law of propagation of light. For if the velocity of light in empty space is to be a quantity that is independent of the choice (or, respectively, of the state of motion) of the inertial system to which it is referred, no absolute meaning can be assigned to the conception of the simultaneity of events that occur at points separated by a distance in space. Rather, a special time must be allocated to every inertial system. If no co-ordinate system (inertial system) is used as a basis of reference there is no sense in asserting that events at different points in space occur simul taneously. It is in consequence of this that space and time are welded together into a uniform four-dimensional continuum.
Progress has been made towards this anticipated unification, but the theories are, as yet, not entirely definitive. The chief trouble is that electro-magnetism cannot be fully treated without entering into problems of electrons and the fine structure of matter; so that the field theory is held back pending developments in our understanding of atomic physics and quanta. The best known unified field theory is that of H. Weyl, proposed in 1918.
He showed that a rather more general geometry than that of Riemann affords place for four coefficients additional to the ten and that these can be identified with the four electro magnetic potentials. A further development and reconstruction was given by A. S. Eddington in 1921. Starting from an "affine geometry" of the most general type, he found that a world tensor can be derived which breaks up into a symmetrical and anti symmetrical part. The symmetrical part provides a Riemannian metric, and therefore comprises space, time and gravitation; the antisymmetrical part furnishes the electromagnetic field. Thus, whilst the gravitational and electromagnetic fields are seen to arise from a single background, the bifurcation is recognized to be very deep-seated. Einstein proposed certain developments and modifications of this theory in 1923.
Early in 1929 Einstein announced that he had reached a new solution of this problem of unification; and there was much public curiosity as to his new theory. There is little that can be said of a non-technical character about it, since the differences from previous unified theories can only be realized by experts, and its attractiveness (or otherwise) depends on the relative simplicity of the mathematical formula which expresses the field-law. In fact, the whole point left unsettled was the particular form of the mathematical expression, so that an exposition of Einstein's latest theory, which leaves out the mathematics, leaves out its main point. It may be said, however, that Einstein's geometrical foundation is a Riemannian geometry coupled with a postulate of distant parallelism. If two ships are near together we can say whether they are or are not sailing on parallel courses; but if they are some thousands of miles apart there is no meaning or definition of what shall be called parallel courses. Similarly, in Riemannian geometry there is no distant parallelism. Einstein postulates that although, conformably to Riemannian geometry, we cannot define parallel lines at a great distance apart by ref erence to space measures alone, by taking also into account elec trical measurements a unique definition can be given. By con spiring to provide this distant parallelism the electromagnetic and gravitational quantities are brought into association. The theory has not yet been fully worked out, and judgment must be suspended as to whether it will satisfy all requirements.
(A. S. E.)