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The Neutron Mass Calculation From Symmetry
and
The Calculation of the Fine Structure Constant from Symmetry
Sandborn, M.,T.
Preface:
The wave equations beginning with Maxwell set the conditions for
locating the symmetry center of the numerical universe. The symmetry center sets the conditions for the transformation from traveling electromagnetic waves to spinning electromagnetic waves (change from boson to fermion). At symmetry, a natural gap exists between the anti-node of the undertone energy process and the anti-node of the overtone energy process. A second wave is added to bridge this energy gap. This second wave or bonding wave is responsible for introducing the second axis of rotation that causes spinning in place rather than traveling motion. The bonding wave must also be accounted for in the calculation of the reference particle wave, and it must be accounted for in the calculation of the fine structure constant as a participant in the reference wave frequencies. Using a particular choice of bonding wave construction it can be shown that when the bonding wave is applied to the harmonic structure defined by
Sandborn1 that the neutron mass can be calculated to within 11.9 millions of a percent of the experimental mass, the proton mass can be calculated exactly (zero deviation from experimental value), the electron can be calculated to within 19.8 millionths a percent, and the fine structure constant can be calculated exactly (zero percent deviation from experimental value).
Supposing that the following selection of waves and their subsequent ratios is not correct. An observation can be made that a bonding wave having a relative percentage composition of approximately 0.0108% undertone and 0.6926% overtone relative to the symmetry wave energy will produce the experimental value of the fine structure constant. Further, the 0.6926% value for the overtone bonding wave will produce the correct addition to the symmetry wave required to obtain the proton,
electron and neutron experimental mass values well within the margin of error. This paper is submitted more as a general observation of the relationship between the calculated symmetry center, the mass calculations, and the fine structure constant, with a theoretical attempt to show how the numbers
might be derived. It is noted that this author believes the
bonding wave structure should be simpler than the following
presentation.
Relevant Information: Sandborn has related pending patents.
Main:
E is defined as the amplitude property of the electromagnetic wave. However, the amplitude property is incomplete as the energy equations are designed around symmetry particles rather than unsymmetrical traveling electromagnetic waves. Since symmetry particles are half-wave cycles rather than complete
wavelengths2,3,4, the value E must be adjusted to account for a full wavelength. Since the amplitude property of the wave is defined to be overtone in
nature2,5, then the overtone wavelength is accounted for by adding
B to the original 1, where 1 represents the reference energy of the nodal position and
B represents the reference energy of the anti-node (FIG. 1). 
E or l is then divided by (1+B) so that the symmetry relativity between
E and l can be accurately defined. The energy conversion equation
E = hc/l, is then changed under symmetry conditions to read: 
The reference harmonic wave is defined in the harmonic structure of
Sandborn1 to have a reference value of 1. This reference value includes a bonding wave. Therefore, in order to obtain the reference 1 value from the symmetry energy, the additional bonding wave energies must be accounted for.
The additional bonding waves can be found by considering the general construction of a symmetry electromagnetic wave (FIGs. 2,3). The symmetry electromagnetic wave is composed of an overtone harmonic process and an undertone harmonic process (shown as a wave form). Each half-wave cycle is separated in symmetry at the energy process anti-nodes. A new wave is then required to bridge the gap created at symmetry. 
Once the reference particle is formed and defined as an overtone reference particle, then an undertone particle is formed as its symmetry
pair1. The fine structure is fundamentally derived from the union of overtone and undertone processes within the electromagnetic
wave2,5. The overtone wave is the amplitude modulated wave and the undertone wave is the modulating wave. Since the particle structure is founded upon the electromagnetic wave, it is reasonable to consider that the particle structure will simply be an advanced electromagnetic wave structure and will exhibit the same basic principle of overtone and undertone relationships. Thus there will exist an overtone reference particle and an undertone reference particle, with the fundamental separation of wavelengths defined by ¸/128. Accordingly, the overtone particle will be defined to begin at the reference 1, and the undertone particle will begin at the reference 1/128 = ¸/256 (FIG. 4). 
The basic fine structure calculation is the average of the calculations from the high and low energy positions of the harmonic symmetry particles. 
The resultant ratio 136.078772 is clearly relatively close to the inversion fine structure constant 137.035999, and the bonding wave frequency has not yet been accounted for.
The calculation of the bonding waves involves two steps: the calculation of the overtone particle bonding waves followed by the calculation of the undertone bonding waves. The reason for the particular order is that the undertone particle bonding waves are a simple multiple of the overtone particle bonding waves.
The first bonding wave or first tier bonding wave is composed from two alternating systems, one overtone and one undertone. The overtone wave is defined as having a reference energy of 5 the reference 1 (the length between H and B is 0 of 1 (FIG. 6), but since the reference harmonic length of 1 is defined by the distance between 1 and 1, then the ratio is revised by half to 5). The total bonding energy is divided between the first and second cycles, and prime and retrograde-prime spins of the alpha wave, thus it is further reduced by half to 0 and by half again to 1/24. Furthermore, since the added wave is 5 the reference wave it will only be operational 5 of the time which means 1/24 is divided by 6 to obtain1/144. This means that the energy addition that must be accounted for is 1/144 the reference energy of 1.
The simultaneous union of overtone and undertone waves requires a combination of overtone and undertone bonding waves. The fundamental way to locate an overtone and undertone wave within the same energy range is to multiply the undertone reference wave by 90 where 90¸/128 = 45¸/64 = 0.9943689... The two values of 1 and 0.9943689 represent the two energy multipliers of the 1/144 bonding energy. Since both values will not be active at the same time, the average of the values is used to calculate the bonding energy. 
The relative value of the new overtone wave is a move from 5 to 0 which is an energy change of 0 (compared with the total distance between H and B equaling 0). The new wave positions are then calculated and shown in FIG. 6. 
The formation of a bonding wave introduces a second tier of bonding waves, identical to the first tier bonding waves, that fill the energy gaps created by the first tier bonding waves. FIG. 7 shows the 2nd tier bonding waves. Each tier 2 bonding wave is the inverse of the tier 1 bonding wave. The inverse is calculated by dividing the wave by 45¸/64 (i.e., the tier 1 wave is shifted below a reference 1, and the new division for tier 2 causes the tier 2 waves to shift above a reference 1. This pattern of reference reversal occurs with each new level of bonding waves). 
The value of the tier 2-B-1 wave begins at 144th of the tier 1 bonding wave given that it is bonding the original bonding wave that functions at 144th of the reference 1 value. The physical length of the 2-B-1 bonding wave is 1/36 of the reference value which means it will operate 1/36 of the time, and it is further divided between first and second cycles and prime and retrograde spins for another 1/4 division, and further divided by 2 given that it bonds only one of the tier 1 waves. The total divisions work out to
1/(2x1442). The equation for this wave is presented in the context of the reference wave. 
The tier 2-A-1 wave begins with the 1/144 division from the tier 1 bonding waves. It represents the difference between the 5 position and the 15¸/128 position. This difference is then multiplied by 1/((45¸/64+1)/2). Since each of the tier 2-A waves are the same except for their relative position, The total tier 2-A waves can be calculated by multiplying by (1+H+B+1). The fact that the Tier 2-B waves also use the connecting tier 2-A-2 and 2-A-3 waves means that they must be accounted for. Since the tier 2-B waves operate 1/144 of the time, the additional use of the 2-A-2 and 2-A-3 waves is 144th of their original value. 
Each tier 2 wave will have its own second tier waves that form the third tier of waves. The tier 2-A waves will have an anti-node bonding wave identical to the tier 2-B but adjusted for size and frequency, and another that is 64/45¸ of its value. A tier 3-B type wave is 144th its reference wave value. For example, the tier 3-B wave generated from a tier 2-A-1 wave is the 2-A-1value divided by 144. Since the calculation has moved from tier 2 to tier 3, the new layer of waves is multiplied by 45¸/64. 
The type 3-A waves generated by the tier 2-A waves are formed by squaring the reference wavelength (5-(15¸/64))2 (This is done to account for the reference length and the time limitation. As described in previous examples, a wave of a ratio length will only operation that same ratio of time). The 3-A waves are then divided by the original 144 time:length division, then multiplied by (1+H+B+1)2 [the tier 2-A waves were multiplied by (1+H+B+1), and each type 3 wave is also multiplied by (1+H+B+1)]. Finally the waves are multiplied by the overtone:undertone ration (1+45¸/64)/2. Added to this is 144th the value of the H and H positions. 
The type 3-B waves generated by the tier 2-B waves are calculated as (45¸/64)/144 and (64/45¸)/144 of the type 2-B waves. 
Additional tiers can be calculated but they cease to effect calculations within experimental error and can be ignored .
All previous calculations are bonding divisions of the overtone reference particle. Similar calculations must be made for the undertone reference particle. The first step is to find the multiplier for the bonding waves that will convert them to the undertone particle. The base undertone particle calculation is ¸/128. This position however does not reference 1, but instead references 1 or 1/128, which means that the reference divisor must be multiplied by 2 since the divisor is twice the new reference compared to the old reference (i.e., 2¸/128 = ¸/64). Also, the relationship has changed from being half a wave cycle under to half a wave cycle over, in which case the real frequency reference is the midpoint. The wave is then divided by the reference midpoint which is ¸. The total changes to the overtone waves are 64¸/¸ = 64. Each overtone wave is then divided by 64 to arrive at the undertone bonding wave calculations. Depending on the tier this divisor is applied to, a multiple of 45¸/64 will be applied. For example, the tier 1 wave is converted by 45¸/642, the tier 2 waves are converted by 1/64, the tier 3 waves are converted by 45¸/642, and the tier 4 waves are converted by 1/64. 
The overtone and undertone bond calculations multiplied together is: = 1.00703436505
The base inversion constant multiplied by the bond calculations is 137.03599976
This calculation matches the experimental value of 137.03599976 with zero deviation. (The number calculated is actually 137.0359997574 but the 574 must be rounded up to 600 given the limitation of the experimental significant digits. This number does not include additional bonding values at E-10 and smaller which will incur very slight changes).
*****
In the calculation of the overtone reference particle, only the overtone multiplier of 1.00692570815 is used. The reference particle includes the bonding energy which means the symmetry wavelength needs to be divided by the bonding multiple in order to arrive at the reference wavelength.
Each particle is formed relative to the reference sub-particle as a series of interconnecting harmonic multiples or divisions. Each particle can then be defined by summing up the multiples and divisions relative to the reference 1 wave. The mass of each particle can then be found by multiplying the reference energy by the particular particle harmonic reference number.
The harmonic structure of the proton defined by Sandborn1 is
432.442093 times the reference 1 mass.
3.86785312 E-30 kg x 432.442093
= 1.6726225 E-27
kg
1.6726231 E-27 kg is 35 millionths of a percent deviation from the experimental
value6 1.6726231 E-27 kg. The range of experimental error is
1.6726241 E-27
kg to 1.6726221 E-27 kg. The harmonically calculated mass from the symmetry energy is
40% inside the experimental error range.
The harmonic structure of the neutron defined by Sandborn1 433.038266 times the reference 1 mass.
3.86785312 E-30 kg x 433.038266 = 1.6749284 E-27
kg
1.6749284 E-27 kg is 11.9 millionths of a percent deviation from the experimental
value6 1.6749286 E-27 kg. The range of experimental error is 1.6749296 E-27
kg to 1.6749276 E-27 kg. The harmonically calculated mass from the symmetry energy is 80% inside the experimental error range.
The harmonic structure for the electron defined by Sandborn1 is 0.23551535 times the reference 1 mass.
3.86785312 E-30 kg x 0.235515352 = 9.1093879 E-31
kg
9.1093879 E-31 kg is 19.8 millionths of percent deviation from the experimental
value6 9.1093897 E-31 kg. The range of experimental error is 9.1093951 E-31
kg to 9.1093843 E-31 kg. The harmonically calculated mass from the symmetry energy is 67% inside the experimental error range.
Observations:
The particle mass and fine structure calculations are dependent upon the harmonic particle structure defined by Sandborn and
Sandborn1, and upon the particular wave structure chosen for the bonding waves. However, it should be observed that because the particle calculations are dependent upon the overtone bond calculations only, and the fine structure constant calculation is dependent upon both the overtone and undertone calculations, then a correct value for both calculations requires at the very least the same ratio between overtone and undertone bonding wave calculations as proposed in the bonding wave structure of Sandborn, and further suggests in principle that the symmetry center calculation and the concept of the bonding wave and the proposed overtone/undertone bonding wave ratios is correct.. It does
not mean that the particular method presented in this essay is correct.
Bibliography
1 Sandborn, M.T., Sandborn, M.D. The Harmonic Formation of the Proton, Electron and Neutron, unpublished paper
2 Sandborn, M.T., Sandborn, M.D. Harmonic Color, Numbers, and the Electromagnetic Wave, unpublished paper
3 Sandborn, M.T., Sandborn, M.D. The Formation of the Particle Alpha Wave, unpublished paper
4 Sandborn, M.T., Sandborn, M.D. The Unified Wave Theory, Undertone 1st Edition, Atlanta: MS Squared, 2001
5 Sandborn, M.T., Sandborn, M.D. An Hypothesis for Undertones as Amplitude Modulation, unpublished paper
6 P. J. Mohr and B. N. Taylor, "The 1998 CODATA Recommended Values of the Fundamental Physical Constants, Web Version 3.1," available at physics.nist.gov/constants (National Institute of Standards and Technology, Gaithersburg, MD 20899, 3 December 1999).
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