The Nature of a Transverse Wave in Relation to the Aether
A transverse wave moves through a medium while the particles of the medium move back and
forth perpendicular to the direction of the disturbance itself. Another way of saying this is: A wave
is transverse if the oscillation of the particles conveying the wave move perpendicular to the
direction in which the wave is traveling.
By Hooke’s law a taut string provides a restoring force that is proportional to the displacement of the string
from its equilibrium position: the greater the displacement the greater the force that tends to restore the
equilibrium. Thus, when a string is made to wave transversally, each atom of the string reacts by trying to
restore its initial horizontal taut state. But when a particle at the top of the crest moves down to restore its
central equilibrium position, the particle goes beyond this position because of its accumulated momentum—
reaching the bottom of a trough. Thus, as long as the string is made to wave, the particles oscillate with
simple harmonic motion—that is, repeatedly, up-down-up-down, from crest to trough, trough to crest.
Source:
Aethro-Kinematics
Definition of a Transverse Wave
These diagrams show how a point on a transverse wave oscillates (up-down-up-down) perpendicular to the direction of the wave.
Adapted fromSource: Principles of Physics: Third
Edition
p. 437
Source: Principles of Physics: Third Edition p. 436
It is no coincidence that these diagrams use a taut string with one end attached to a wall and the other
made to oscillate up and down by the motion of a hand. The transverse wave theory of light was based
on wave-motion of a taut string.
Hooke's Law: The Restoring Force of a Transverse Wave
It is the electromagnetic bond between the
atoms that make up a taut string that provide
the "restoring force." They are what keeps the
string in tact--that is, make it possible for one
point on the string to oscillate up and down,
since when it reaches the apex of the crest,
the neighboring atoms pull it back down. The
string taut represents the equilibrium position.
Since the particles of the aether would move up and down, perpendicular to the direction of the wave
through space, the "restoring force" would be resemble for that oscillating up-down-up-down motion.
That is, the "force" would not be a mechanical one involving collisions, but a mysterious action that
caused the aether particles involved in the wave to oscillate. This is an absolutely impossible condition
if one is not ready to admit such an unlikely "force."
The Impossibility of an Aether with Restoring Forces
Source: Principles of Physics: Third Edition p. 555
Source: Principles of Physics: Third Edition p. 440
The circled particle is called Particle T.

If Particle T were moving down from T = 1 to T =
5, it would be colliding with aether particles
below it, and would rebound upwards upon
those collisions. However the transverse wave
theory requires the particle to keep moving
down until it reaches its trough. But at T = 6,
what is causing Particle T to move upwards
again? The aether particle from "below" it
would need to collide with it for it to move
upwards. But what would cause
that particle to
move upwards?

There is nothing in the transverse wave theory
of light that could account for this "restoring
force" -- i.e., the movement of the aether
particle from crest to centerline, and trough to
centerline.

It is impossible for an aether particle to move
up and down like this when part of a medium
made up of freely (unbonded) aether particles.
There is no "force" that exists between aether particles. There is no "bond." The only way they interact
is through collisions. These essential facts make it impossible for the aether medium to support
transverse waves.
If we imagine the blocks to be aether particles, and imagine that the aether fills the space above the
particles depicted here, what would push the trough up to the centerline of the wave? What would
push the crest towards the centerline? For, according to inertia, if the aether particles moved up, the
disturbance would be distributed in the "up" direction. Yet, somehow, the aether must defy the
principle of inertia, and cause the disturbance to propagate forward, to the right. Somehow, the
up-down motion of the wave does not disturb the aether above and below the wave.
Source:
Author
It is the radial force (pulling on the string)
that makes the string taut. It is this taut state
that is the "equilibrium" position that the
string tries to restore.
No such thing as
"pulling the aether taut" exists.
Young and Fresnel proposed that the aether needed to have enough rigidity to supply the forces to
oppose the distortions produced by the waves. In other words, the aether, if a mechanical system,
could not be a fluid; it had to be a solid.
This animation shows how a particle in a transverse wave oscillates (up-down-up-down)
perpendicular to the direction of the wave.
The Proposed Cause (Motion) of this Wave
The electron is said to oscillate. The electron is hypothesized to move up and down like the man's hand
holding the string. This type of oscillatory motion is also an impossible condition of the motion of an electron.