Of absolute perfection.”
Einstein’s Theory of Relativity has led to determining a key law of nature—the law of gravitation—which is also the basic law of mechanics. Thus it embraces a whole realm of physics, and promises, through the researches of Professor Weyl, to embrace another realm—electro-dynamics. Its limitations are not yet reached, for Einstein has already postulated therefrom a theory of a finite, yet unbounded, universe. This essay, however, is mainly concerned with mechanics, and electrical forces are not considered.
To have synthesised Newton’s two great principles—his law of motion and law of gravitation—interpreting in the process the empirical law of equality of gravitational and inertial mass, is alone an immense achievement; but Einstein’s researches have opened up a new world to the physicist and philosopher which is of greater importance. He has given us a vision of the immaterial world, a geometrical or mathematical vision, which is more satisfying than the “ether” conceptions hitherto presented. The fabric of his vision is not baseless. It is this fabric we shall consider, touching on certain aspects of the Einstein theory in the endeavor to present an image in miniature of his edifice of thought and to show the firmness of its foundations. That they are well and truly laid was demonstrated by the verification, from observations made during the solar eclipse in 1919, of Einstein’s prediction of the displacement of a wave of light in a gravitational field, showing light to have the property of weight.
The physical world is shown by Einstein to be a world of “relations.” Underlying it there is an absolute world of which physical phenomena are the manifestation. “Give me matter and motion,” says Descartes, “and I will construct the world.” “Give me a world in which there are ordered relations,” says the Relativist, “and I will show you the behavior of matter therein” (mechanics). We first view this underlying world as an abstraction, abstracting energy (“bound” as in matter and electrons, “free” as in light), and its attribute force. This abstraction we will call the “World-Frame.” Later, we will study the underlying world in connection with energy, and will call this absolute world the “World-Fabric.” The connection between the geometrical character of the World-Frame and the geometrical characters of the World-Fabric is the key to the law of gravitation.
The World-Frame
This is our conception of a world, if such were possible, entirely free from the influence of energy. We may conceive of it as an amorphous immaterial something containing “point-events” (a point-event being an instant of time at a point in space—a conception, not a definition). These point-events have a fourfold order and definite relation in this Frame, i.e. they can be specified by four variables or coordinates in reference to some base called a reference system, with respect to which they are forward or backward, right or left, above or below, sooner or later. This shows the World-Frame to be four-dimensional. Thus an aggregate of point-events (or an “event,” which implies limited extension in space and limited duration in time)[1] would have what we familiarly describe as length, breadth, height and time. To express these metrical properties most simply we must choose a four-dimensional reference system having a particular form—rectilinear axes (Cartesian coordinates), and a particular motion—uniform and rectilinear, i.e. unaccelerated, and non-rotating with respect to the path of a light ray. We call this an inertial system because Newton’s Law of Inertia holds for such a system alone. This system indicates how observers partition the World-Frame into space and time. It restricts observers to uniform rectilinear motion, and observations to bodies and light-pulses in such motion. Thus gravitational and other forces are discounted, and we obtain World-Frame conditions notwithstanding the fact that observers are in the presence of energy.
Now the separation between point-events which have a definite relation to each other must be absolute. The separation between two points in a plane is defined by the unique distance between them (the straight line joining them). Between point-events the analogue of this unique distance, which we call the “separation-interval” (to indicate its time-like and space-like nature), is also unique. Its unique and absolute character give it great importance as thereby it is the same for all observers regardless of their reference system.
If, in place of the rather cumbersome expression
