Note Note 4 — III EINSTEIN

For the benefit of those readers who wish to gain a deeper insight into the relativity principle, we shall here discuss it very briefly.

Newton and Galileo had developed a relativity principle in mechanics which may be stated as follows: If one system of reference is in uniform rectilinear motion with respect to another system of reference, then whatever physical laws are deduced from the first system hold true for the second system. The two systems are equivalent. If the two systems be represented by xyz and , and if they move with the velocity of v along the x-axis with respect to one another, then the two systems are mathematically related thus: (1)(1)

and this immediately provides us with a means of transforming the laws of one system to those of another.

With the development of electrodynamics (which we may call electricity in motion) difficulties arose which equations in mechanics of type (1) could no longer solve. These difficulties merely increased when Maxwell showed that light must be regarded as an electromagnetic phenomenon. For suppose we wish to investigate the motion of a source of light (which may be the equivalent of the motion of the earth with reference to the sun) with respect to the velocity of the light it emits—a typical example of the study of moving systems—how are we to coordinate the electrodynamical and mechanical elements? Or, again, suppose we wish to investigate the velocity of electrons shot out from radium with a speed comparable to that of light, how are we to coordinate the two branches in tracing the course of these negative particles of electricity?

It was difficulties such as these that led to the Lorentz-Einstein modifications of the Newton-Galileo relativity equations (1). The Lorentz-Einstein equations are expressed in the form: (2)(2)

c denoting the velocity of light in vacuo (which, according to all observations, is the same, irrespective of the observer’s state of motion). Here, you see, electrodynamical systems (light and therefore “ray” velocities such as those due to electrons) are brought into play.

This gives us Einstein’s special theory of relativity. From it Einstein deduced some startling conceptions of time and space.