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 RS—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 T_a is the first rotation, and T_b is the second rotation (T = “Turn”, the counterspace name for a rotation):

T_a = e^{–i (kx)} = cos (kx) – i sin (kx)

T_b = e^{–i (–kx)} = cos (kx) + i sin (kx)

The shift (separation) between them then becomes:

y (x) = e^{–i kx} + e^{i kx} = 2 cos (kx)

Which shows that the shift between the two turns is expressed as a “cosine” wave—the “linear vibration” of Larson.

Calculation of Frequency

First, the two turns (rotations) represent the 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/T_a² - 1/T_b² (Where T_a and T_b 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/T_a² - 1/T_b²) (in natural units)

Then, 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/T_a² - 1/T_b²) (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 T_a to unit speed, 1, and vary the speed of T_b, 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 and polarization, along with all the associated effects due to the bi-rotating turns.

The electromagnetic frequency spectrum as multiples of the natural unit of space.

Reciprocal System

	Radio						Reciprocal System
Range	Wavelength	Frequency	Band	Common	Application		Unit Space Multiplier
	8.404955×1011 m	0.0003566854 hz	Maximum wavelength / Minimum frequency boundary				s × 2568
	3.283186×109 m	0.09131146 hz					s × 2567
L F r a d i a t i o n			ULF	3.5 hz	Brain Asleep
				4.0 hz	Theta Brain
				7.0 hz	Hypnogogic state
				7.5 hz	Schumann Resonance of Earth
				8.0 hz	Alpha Brain
				13.0 hz	Awake Brain
				14.0 hz	Beta Brain
	12.825 Mm	23.376 hz					s × 2566
			ELF	30.0 hz	Agitated Brain
				30-300 hz
			VF	300-3000 hz
	50.097 km	5.9842 khz					s × 2565
			VLF	3-30 khz	ITU Band 4
			LF	30-300 khz	ITU Band 5
			MF	300-1500 khz	AM 530-1720 khz	ITU Band 6
	195.69 m	1.5320 Mhz					s × 2564
				1500-3000 khz	Short-wave Radio
			HF	3-30 Mhz	ITU Band 7
			VHF	30-300 Mhz	ITU Band 8
	0.76443 m	392.18 Mhz					s × 2563
			UHF	0.3-3 Ghz	ITU Band 9
			SHF	3-30 Ghz	ITU Band 10
			EHF	30-300 Ghz	ITU Band 11
	2.9860 mm	100.40 Ghz					s × 2562
			Sub-millimeter	300-3000 Ghz	ITU Band 12
			Far Infrared	3-30 Thz
	11.664 um	25.702 Thz			Larson's Unit Frequency		s × 2561
			Near Infrared
	729 nm	411.23 Thz		750 nm			s × 16
			V I S I B L E		Dark Red
	683 nm	438.65 Thz		680 nm			s × 15
					Light Red
	638 nm	469.98 Thz		610 nm			s × 14
					Orange
	592 nm	506.13 Thz		590 nm			s × 13
					Yellow
	548 nm	548.31 Thz		570 nm			s × 12
					Green
	501 nm	598.15 Thz		500 nm			s × 11
					Blue
	456 nm	657.97 Thz		450 nm			s × 10
					Indigo
	410 nm	731.08 Thz		410 nm			s × 9
					Violet
	365 nm	822.46 Thz		360 nm			s × 8
			uV		Near Ultraviolet
	182 nm	1.6449 Phz		200 nm			s × 4
				3-30 Phz	Vacuum Ultraviolet
	45.563 nm	6.5797 Phz					Unit Space s × 2560
H F r a d i a t i o n			Soft X-Rays	30 Phz 3 Ehz
	177.98 pm	1.6844 Ehz					s × 256-1
			Hard X-Rays	3-30 Ehz
			Soft Gamma Rays	30-300 Ehz
	695.24 fm	431.21 Ehz					s × 256-2
			Hard Gamma Rays	300 Ehz 3 Zhz	(Urantia - atomic)
	2.7158 fm	110.39 Zhz					s × 256-3
			Cosmic Rays	3-??? Zhz	(Urantia - pre-atomic)
	10.609 am	28.260 Yhz					s × 256-4
			Ultimatonic		(Urantia - particle formation)
	41.440 zm	7.234 Xhz					s × 256-5
			InfraUltimatonic		(Urantia - ultimaton formation)
	161.972 ym	184.049 Xhz					s × 256-6
	632.313 xm	474.119 Lhz					s × 256-7
	2.470×10-27 m	121.375×1033 hz	Minimum wavelength / Maximum frequency Boundary				s × 256-8

 

The following table shows the breakdown of natural units of wavelength and frequency--multiples of 256 units of space and time. There appear to be 7 major density groupings of the speeds in both the material and cosmic sectors. Band 8/-8 would therefore be the minimum and maximum bounds for frequency of photons. Also see the EM Frequency Spectrum for details on each band.

Photon Density Bands

Sector	Band	Wavelength (meters) (s × 256band)	Wave duration (seconds) (t × 256band)	Frequency (hz) (1/wave duration)	Density
M-Limit	8	8.404955×1011	2.803591×103	3.566854×10-4		8
Material space/time LF	7	3.283186×109	1.095153×101	9.131146×10-2	7
	6	1.282494×107	4.277941×10-2	2.337573×101		6
	5	5.009744×104	1.671071×10-4	5.984188×103	5
	4	1.956931×102	6.527620×10-7	1.531952×106		4
	3	7.644262×10-1	2.549851×10-9	3.921797×108	3
	2	2.986040×10-3	9.960357×10-12	1.003980×1011		2
	1	1.166422×10-5	3.890764×10-14	2.570189×1013	1
Unit boundary	0	4.556335×10-8	1.519830×10-16	6.579684×1015		0
Cosmic time/space HF	-1	1.779818×10-10	5.936835×10-19	1.684399×1018		2
	-2	6.952416×10-13	2.319076×10-21	4.312062×1020	3
	-3	2.715787×10-15	9.058892×10-24	1.103888×1023		4
	-4	1.060854×10-17	3.538630×10-26	2.825953×1025	5
	-5	4.143963×10-20	1.382277×10-28	7.234439×1027		6
	-6	1.618735×10-22	5.399520×10-31	1.852016×1030	7
	-7	6.323185×10-25	2.109188×10-33	4.741162×1032		8
C-Limit	-8	2.469994×10-27	8.239014×10-36	1.213737×1035

Color Key

	Transition point to next octave (Material space/time and Cosmic time/space frequency limit).
	Reciprocal System unit boundary, also called "unit speed" where the transition from Material (space/time) to Cosmic (time/space) occurs.
	Densities known and explored by legacy science.
	Densities not yet explored by legacy science.