Part 9

Note 3 (page 30)

Sir Oliver Lodge goes to the extreme of pinning his faith in the reality of this ether rather than in that of matter. Witness the following statement he made recently before a New York audience:

"To my mind the ether of space is a substantial reality with extraordinarily perfect properties, with an immense amount of energy stored up in it, with a constitution which we must discover, but a substantial reality far more impressive than that of matter. Empty space, as we call it, is full of ether, but it makes no appeal to our senses. The appearance is as if it were nothing. It is the most important thing in the material universe. I believe that matter is a modification of ether, a very porous substance, a thing more analogous to a cobweb or the Milky Way or something very slight and unsubstantial, as compared to ether."

And again:

"The properties of ether seem to be perfect. Matter is less so; it has friction and elasticity. No imperfection has been discovered in the ether space. It doesn't wear out; there is no dissipation of energy; there is no friction. Ether is material, yet it is not matter; both are substantial realities in physics, but it is the ether of space that holds things together and acts as a cement. My business is to call attention to the whole world of etherealness of things, and I have made it a subject of thirty years' study, but we must admit that there is no getting hold of ether except indirectly."

"I consider the ether of space," says Lodge, in conclusion, "the one substantial thing in the universe." And Lodge is certainly entitled to his opinion.

Note 4 (page 51)

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 $x'y'z'$, 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:

$$x' = x - vt, y' = y, z' = z, t' = t,$$

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:

$$x' = \frac{x-vt}{\sqrt{1-\frac{v^2}{c}}}, y' = y, z' = z, t' = \frac{t-\frac{v}{c^2}\cdot x}{\sqrt{1-\frac{v^2}{c^2}}},$$

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.

Note 5 (page 55)

The velocity (v) of an object in one system will have a different velocity (v') if referred to another system in uniform motion relative to the first. It had been supposed that only a "something" endowed with infinite velocity would show the same velocity in all systems, irrespective of the motions of the latter. Michelson and Morley's results actually point to the velocity of light as showing the properties of the imaginary "infinite velocity." The velocity of light possesses universal significance; and this is the basis for much of Einstein's earlier work.

Note 6 (page 56)

"Euclid assumes that parallel lines never meet, which they cannot do of course if they be defined as equidistant. But are there such lines? And if not, why not assume that all lines drawn through a point outside a given line will eventually intersect it? Such an assumption leads to a geometry in which all lines are conceived as being drawn on the surface of a sphere or an ellipse, and in it the three angles of a triangle are never quite equal to two right angles, nor the circumference of a circle quite times its diameter. But that is precisely what the contraction effect due to motion requires."

(Dr. Walker)

Note 7 (page 57)

Einstein had become tired of assumptions. He had no particular objection to the "ether" theory beyond the fact that this "ether" did not come within the range of our senses; it could not be "observed." "The consistent fulfilment of the two postulates--'action by contact' and causal relationship between only such things as lie within the realm of observation [see Note 2] combined together is, I believe, the mainspring of Einstein's method of investigation...." (Prof. Freundlich).

Note 8 (page 59)

That the conception of the "simultaneity" of events is devoid of meaning can be deduced from equation (2) [see Note 4]. We owe the proof to Einstein. "It is possible to select a suitable time-coordinate in such a way that a time-measurement enters into physical laws in exactly the same manner as regards its significance as a space measurement (that is, they are fully equivalent symbolically), and has likewise a definite coordinate direction.... It never occurred to anyone that the use of a light-signal as a means of connection between the moving-body and the observer, which is necessary in practice in order to determine simultaneity, might affect the final result, i.e., of time measurements in different systems." (Freundlich). But that is just what Einstein shows, because time-measurements are based on "simultaneity of events," and this, as pointed out above, is devoid of meaning.

Had the older masters the occasion to study enormous velocities, such as the velocity of light, rather than relatively small ones--and even the velocity of the earth around the sun is small as compared to the velocity of light--discrepancies between theory and experiment would have become apparent.

Note 9 (page 67)

How the special theory of relativity (see Note 4) led to the general theory of relativity (which included gravitation) may now be briefly traced.