Photons
Posted: Fri Sep 10, 2004 11:13 pm
Given the nature of rotational space (counterspace), the first manifestation with RS2 is therefore the positron, not the photon as Larson had predicted. So where does that put the RS2 photon, and how does it differ from Larson's original conception?
When a second rotational motion occurs within the time region, the rotations will interact in conformance with complex Euler relations regarding rotation. The result is not rotation, but a cosine wave -- a "simple harmonic motion."
Here we must distinguish between primary and secondary motions. In rotational space, "rotation" is primary, "linear" is secondary and can ONLY occur as a result of a combination of primary motions. Therefore, Larson's "simple harmonic motion" photon NEVER occurs as a consequence of primary motion in RS2 -- only secondary motion. And it is a consequence of TWO rotations, which Nehru refers to as a "bi-rotation". (See Nehru's articles on bi-rotation for the consequences of this rotational model, including linear and circular polarization, the Zeeman effect and others).
The photon bi-rotation, like interlocked gears, move in opposite directions and are expressed as complex Euler relations, where Ta is the first rotation, and Tb is the second rotation (T = "Turn", the counterspace name for a rotation):
Ta = e–i(kx) = cos kx – i sin kx
Tb = e–i(–kx) = cos kx + i sin kx
The shift (separation) between them the becomes:
y(x) = e–ikx + eikx = 2 cos kx
Which shows that the shift between the two turns is expressed as a "cosine" wave -- the "linear vibration" of Larson.
Now to the frequency.
First, the two turns (rotations) represent the temporal speeds of the photon. To determine the wavelength, one must simply compute the shift between the two turns. This is done just like a regular angle; subtract the smaller angle from the larger one, and you get the angle between.
Second, "speed" in the time region is different than the time-space region. We normally recognize "s/t" as speed, but, as Larson describes in "Nothing But Motion", p. 155, when inside the unit boundary the "space" aspect is fixed at one unit. But the equivalent space can be computed by s = 1/t. Therefore, a speed of "s/t" in the time-space region becomes a speed of "(1/t)/t = 1/t2" in the time region. Note that in the time region, speed is is 2-dimensional according to Larson and therefore fits the concept of being polar/rotational rather than translational.
To compute our shift, all we have to do is take the difference between the two turn "time region speeds":
dT = 1/Ta2 - 1/Tb2 {Where Ta and Tb are the speeds of the turns.}
Next, we need to translate that shift out of the time region across the unit boundary, so we can determine the equivalent space in order to observe and measure it. That is simply done by (s = 1/t) and taking the reciprocal, 1/dT.
In legacy science, wavelength is 2 units of space, so the final step is to multiply 1/dT by 2, giving 2/dT. Therefore:
wavelength = 2 / dT {in natural units}
wavelength = 2 / (1/Ta2 - 1/Tb2) {in natural units}
Just multiply by unit space to get conventional units.
One may notice the similarity between this wavelength calculation and the formula for computing atomic spectra:
1/wavelength = R (1/m2 - 1/n2) {legacy science}
Where "R" is the Rydberg constant, and "m" and "n" are integers.
Let us convert our wavelength equation to match the inverse wavelength of the atomic spectra formula:
1/wavelength = 0.5 (1/Ta2 - 1/Tb2) {RS2}
Which identifies the Rydberg constant, in natural units, to be 0.5. If you notice in the Euler shift computation above, it is "2 cos kx" -- not just "cos kx", we can see the origin of the Rydberg constant -- the "2" in the formula. (1/2 = 0.5, the Rydberg constant in natural units).
If we set Ta to unit speed, 1, and vary the speed of Tb, we get the equation for the Lyman series of atomic spectra. 2 gives the Balmer series, 3 the Paschen series and 4 the Brackett series.
With this new model of the photon, we can accurately describe, both conceptually and mathematically, wavelength, polarization and atomic spectra, along with all the associated effects due to the bi-rotating turns.
When a second rotational motion occurs within the time region, the rotations will interact in conformance with complex Euler relations regarding rotation. The result is not rotation, but a cosine wave -- a "simple harmonic motion."
Here we must distinguish between primary and secondary motions. In rotational space, "rotation" is primary, "linear" is secondary and can ONLY occur as a result of a combination of primary motions. Therefore, Larson's "simple harmonic motion" photon NEVER occurs as a consequence of primary motion in RS2 -- only secondary motion. And it is a consequence of TWO rotations, which Nehru refers to as a "bi-rotation". (See Nehru's articles on bi-rotation for the consequences of this rotational model, including linear and circular polarization, the Zeeman effect and others).
The photon bi-rotation, like interlocked gears, move in opposite directions and are expressed as complex Euler relations, where Ta is the first rotation, and Tb is the second rotation (T = "Turn", the counterspace name for a rotation):
Ta = e–i(kx) = cos kx – i sin kx
Tb = e–i(–kx) = cos kx + i sin kx
The shift (separation) between them the becomes:
y(x) = e–ikx + eikx = 2 cos kx
Which shows that the shift between the two turns is expressed as a "cosine" wave -- the "linear vibration" of Larson.
Now to the frequency.
First, the two turns (rotations) represent the temporal speeds of the photon. To determine the wavelength, one must simply compute the shift between the two turns. This is done just like a regular angle; subtract the smaller angle from the larger one, and you get the angle between.
Second, "speed" in the time region is different than the time-space region. We normally recognize "s/t" as speed, but, as Larson describes in "Nothing But Motion", p. 155, when inside the unit boundary the "space" aspect is fixed at one unit. But the equivalent space can be computed by s = 1/t. Therefore, a speed of "s/t" in the time-space region becomes a speed of "(1/t)/t = 1/t2" in the time region. Note that in the time region, speed is is 2-dimensional according to Larson and therefore fits the concept of being polar/rotational rather than translational.
To compute our shift, all we have to do is take the difference between the two turn "time region speeds":
dT = 1/Ta2 - 1/Tb2 {Where Ta and Tb are the speeds of the turns.}
Next, we need to translate that shift out of the time region across the unit boundary, so we can determine the equivalent space in order to observe and measure it. That is simply done by (s = 1/t) and taking the reciprocal, 1/dT.
In legacy science, wavelength is 2 units of space, so the final step is to multiply 1/dT by 2, giving 2/dT. Therefore:
wavelength = 2 / dT {in natural units}
wavelength = 2 / (1/Ta2 - 1/Tb2) {in natural units}
Just multiply by unit space to get conventional units.
One may notice the similarity between this wavelength calculation and the formula for computing atomic spectra:
1/wavelength = R (1/m2 - 1/n2) {legacy science}
Where "R" is the Rydberg constant, and "m" and "n" are integers.
Let us convert our wavelength equation to match the inverse wavelength of the atomic spectra formula:
1/wavelength = 0.5 (1/Ta2 - 1/Tb2) {RS2}
Which identifies the Rydberg constant, in natural units, to be 0.5. If you notice in the Euler shift computation above, it is "2 cos kx" -- not just "cos kx", we can see the origin of the Rydberg constant -- the "2" in the formula. (1/2 = 0.5, the Rydberg constant in natural units).
If we set Ta to unit speed, 1, and vary the speed of Tb, we get the equation for the Lyman series of atomic spectra. 2 gives the Balmer series, 3 the Paschen series and 4 the Brackett series.
With this new model of the photon, we can accurately describe, both conceptually and mathematically, wavelength, polarization and atomic spectra, along with all the associated effects due to the bi-rotating turns.