Longitudinal waves are usually considered to be like sound waves in which the producer of the wave creates compressions and rarefications alternately (like a vibrating string) which move away from the source. Transverse waves are waves moving outward from the source but acting at 90 degrees from the direction of outward movement.
Light half-waves are technically longitudinal in the sense that the nether is pulled to create a rarefication (but no compression) which moves outward from the source. This pull is at 45 degrees from the direction of outward travel and has two vectors which, when combined, give the resultant 45 degree wave. One vector is tranverse (the tangential vector) and other (the radial vector) is parallel to the direction of wave travel outward, so the vectors are at 90 degrees to one another. The vector with motion parallel to the outward travel (radial vector) never changes much because each half-wave has the same radial acceleration. So I believe the radial vector may be discounted for practical purposes. The tangential vector alternates direction 180 degrees from one half-wave to the next and creates the transverse waves we call light.
If there are other waves created by the electron, I am not aware of them. However, some physicists in Russia and perhaps in other places talk of longitudinal light waves. Perhaps this is the same type of wave mentioned above and semantics is the only problem - or perhaps there are waves other than the one mentioned above.
The EPR experiments mentioned and explained elsewhere appear to many to indicate that light waves exist which are transmitted instantaneously. According to our research, this is a phenomenon that works in a different manner entirely and is not caused by a longitudinal light wave.
According to Fundamentals of Physics by Halliday, Resnick, and Walker, in 1924, a French physicist, Louis de Broglie, theorized that all matter might actually be waves. Photons were considered to be particles at this time. He suggested that the momentum of a photon, "p", is equal to "h/W" where "h" is Planck's constant and "W" is the wavelength. Today the equation used is
W = h/p
and "W" is called the de Broglie wavelength.
Experiments were made with electron and x-ray beams in which both electron and x-ray beams
appeared to behave like waves.
In 1926, Austrian physicist Erwin Schrodinger described "matter waves" with equations. For a moving "free particle" on which no net force acts, the total energy of the particle is kinetic, so kinetic energy, "Ek", of a particle is also described by the equation
Ek = (1/2)mv2
and its momentum, "p", is also described by the equation
p = mv.
Within Schrodinger's complex equations (not shown herein) is found the de Broglie wavelength.
The Electron Trap
To simulate what happens to an electron within an atom, an "electron trap" was devised which, in principle, was a means of keeping an electron prisoner within the confines of a length "L". The electron could vibrate (move back and forth within this length) within the trap just as the electron within the atom must vibrate within its allotted space. In its "ground state", the electron does not vibrate and no photon is produced. When the electron is energized, it vibrates at quantum state number one, or at a higher quantum state, according to how much energy is introduced. When the electron produces a photon, the quantum state is reduced. Quantum states are given that name because no intermediary states are allowed to exist.
Accepted equations describing the trapped electron follow. "n" is the "quantum number" identifying the "quantum state" of the electron. It appears to be the number of times the electron moves back and forth within the electron trap or the atom.
1. L = nW/2
2. W = h/p
3. p = (2mEn) 1/2
Where En is the kinetic energy of a photon in quantum state "n". Therefore
4. W = h/p = h/(2mEn) 1/2
Substituting equation #4 into equation #1 and solving for En,
5. En = [h2/(8mL2)]n2
"n" must always be a whole number.
The quantum number identifies a quantum state which was once called an energy level or an orbit for the electron. The higher the number for "n", the higher is the quantum state or energy level of the electron. En is a particular kinetic energy level, so
(1/2)mv2 = [h2/(8mL2)]n2
(2/2)m2v2 = (hn/2L)2
mv = hn/2L = p
"n" is the number of full cycles of the electron within the trap or atom, the number of
times it makes a complete circuit to and from the length of the trap. For each complete
circuit (cycle), the electron reverses its direction of motion twice. The light half-wave
is produced by one reversal of electron direction and received as one reversal of electron
direction. For the complete wave, there are two reversals of direction - one at each end of
the electron length of travel. When "n" equals one, the electron is at its first level of
energy and "hn" is merely "h" for one complete wave.
When "n" equals two, the reversals come twice as often, so the electron is moving to and
fro to create two cycles where there was only one before. When "n" equals three, the
reversals come three times as often and the electron is creating three cycles where there
was but one at the beginning. When "n" equals four, the reversals come four times as often
because the electron is creating four cycles where there was one at the beginning. Thus,
the quantum states are musical in nature. Quantum state one is the fundamental of our
"flute of light". Quantum state two is the next octave. Quantum state three is the fifth
in the second octave. And quantum state four is the third octave. Each higher state is
created by "overblowing" in the sense that energy is added. In the flute, the energy is
that of sound and is transmitted by air and additional nodes are added.
In the atom or the electron trap, the energy is that of light, is transmitted by the nether,
and more acceleration, average velocity, and reversals are added.
The Interacting Forces
Three forces are active within the trap or within the atom. One is the electron mouth taking in the nether so that there is a form of propulsion in the direction the mouth is pointed. Second is the like-charges of the other electrons which stop the electron motion at each end of its half-cycle, and propel it into its next half-cycle. Third is the momentum of the electron which acts against any force which attempts to cause the electron to accelerate or decelerate.
At the "ends" of the trap or of the electron space within the atom, the repelling force of the other electrons act very much like springs. If one has ever pushed two like poles of a magnet toward one another, one has felt a similar force. This force becomes stronger as the electron's momentum pushes against it, and it repels the electron more strongly after the electron has penetrated farther into it. Each time the electron is repelled, it accelerates away from this force. As the electron reaches its midpoint of travel, it begins to feel this same force from the electrons at the other end of its journey - and the electron decelerates. It penetrates into the realm of the force and is once again turned to start a new acceleration.
Actually, the end forces extend to infinity, so that the like-charge force at one end is balanced by the like-charge force at the other end, and the electron moves between the two forces like a weight in a pendulum moves between the forces of gravity at the end points of its travel. The length "L" is never really constant, but changes according to the energy used to move the electron. When energy is given to an electron so that it moves to a higher quantum state, the "pendulum" slowly absorbs the energy so that it begins by moving less distance, then eventually swings high. After the higher state is reached and the electron begins produce a photon, the pendulum begins to move less distance again until the complete photon has been produced. It each case, the absorbing of energy and the producing of energy, the period of the pendulum does not change even though the distance traveled changes. Thus, the distance "L" is increased or decreased as the average electron velocity is increased or decreased, and the electron's round trip always happens in the same length of time.
When a receiving electron is given additional energy in the form of more reversals of direction, the reversals provided between those already present (if any are present) cause the present ones to shift within the boundaries of the trap so that equal spacing between the old and the new is achieved. The amplitude of the movements expand quickly to fill the maximum distance for "L" and the spring-like trampoline effect increases the electron speed from one reversal to the next until the higher quantum state has been attained.
When the "pumped up" electron begins to send a photon from a higher quantum state, the
energy sent by each reversal depletes the size of the pendulum-like swing until the energy
is low enough to drop to the next quantum state at which point the lower state with its
fewer reversals per second becomes dominant once more. Higher quantum states have greater
lengths of electron travel than do lower quantum states due to higher average electron
velocities and the consequent higher electron momentums.
1. When a photon adds energy to a receiving electron, it does so by causing the electron to turn around at regular intervals.
2. Each turn-around causes the electron to move away from its end-point with greater acceleration. The spring-like effect of the like-charge in resonance adds to this linear acceleration.
3. Although the first cycle of the receiving electron was weak in linear amplitude, as the resonant process continues, it grows stronger until the distance between end points, the end-point accelerations, and the intermediate average velocities all become much greater.
4. When the last of the incoming photon has exhausted itself, the amplitude between end-points is at its greatest and the receiving electron becomes a sending electron.
5. The energy sent is the energy of end-point acceleration translated into energy to cause the electron to turn around.
6. The above bleeds off energy that might have been used to maintain the end point acceleration and the electron has less average velocity in its travel to the next end point, and less "penetration" into the "spring" at the end-point.
7. This process continues until the energy level (quantum state) is reduced to the next level down.
It is the constant value of the energy release at the turn-around that is the energy of
each half wave of a photon. This is true even though the energy of the linear electron motion
between end-points varies. It might be truthfully stated that the energy of of the linear
electron motion is being removed in "quantum" units at each end-point to create "quantized"
half-wave photon energy.
The reason for the quantization of energy levels is very simple. Electron reversals, to be resonant, must occur at the ends of the electron travel (the ends of the pendulum swings). Therefore, "n" must always be a whole number. Again, this is very much like what happens when one overblows the fundamental of a flute.