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This appendix lists a selection of FUPCONs and juxtaposes their values when using SI, SE, SP, and SG units of measure. The least-significant digit of the listed SI mantissas is rounded. For more-accurate SI values, see the National Institute of Standards and Technology's (NIST's) reference on Constants, Units, and Uncertainty.
| Ratio or Constant | Code | SI | Dimension | SE | SP | SG |
|---|---|---|---|---|---|---|
| Electron...Proton | δ | 1836.15 | none | same as SI | same as SI | same as SI |
| Fine-Structure | β(α-1) | 137.036 | none | same as SI | same as SI | same as SI |
| Electron...Masson | θ | 2.0412 × 1021 | none | same as SI | same as SI | same as SI |
| (Electron...Masson)2 | θ2 | 4.1667 × 1042 | none | same as SI | same as SI | same as SI |
| Electron Mass | me | 9.1094 × 10-31 | M | 1 | δ-1 | θ-1 |
| Elec. Threshold Temp. | ke | 5.9299 × 109 | K | 1 | δ-1 | θ-1 |
| Electron Energy | Ee | 8.1871 × 10-14 | ML2T-2 | 1 | δ-1 | θ-1 |
| Electron Charge | qe | 1.6022 × 10-19 | Q | -1 | N/A | N/A |
| Electron Wavelength | λe | 2.4263 × 10-12 | L | 1 | δ | θ |
| Virtual Elec. Lifetime | te | 8.0933 × 10-21 | T | 1 | δ | θ |
| Proton Mass | mp | 1.6726 × 10-27 | M | δ | 1 | δ θ-1 |
| Prot. Threshold Temp. | kp | 1.0888 × 1013 | K | δ | 1 | δ θ-1 |
| Proton Energy | Ep | 1.5033 × 10-10 | ML2T-2 | δ | 1 | δ θ-1 |
| Proton Charge | qp | 1.6022 × 10-19 | Q | N/A | +1 | N/A |
| Proton Wavelength | λp | 1.3214 × 10-15 | L | δ-1 | 1 | δ-1 θ |
| Virtual Prot. Lifetime | tp | 4.4077 × 10-24 | T | δ-1 | 1 | δ-1 θ |
| Masson Mass | mg | 1.8594 × 10-9 | M | θ | δ-1 θ | 1 |
| Planck Mass | MPl | 2.1767 × 10-8 | M | θ β0.5 | δ-1 θ β0.5 | β0.5 |
| Mas. Threshold Temp. | kg | 1.2104 × 1031 | K | θ | δ-1 θ | 1 |
| Planck Temperature | KPl | 1.4170 × 1032 | K | θ β0.5 | δ-1 θ β0.5 | β0.5 |
| Masson Energy | Eg | 1.6712 × 108 | ML2T-2 | θ | δ-1 θ | 1 |
| Planck Energy | EPl | 1.9563 × 109 | ML2T-2 | θ β0.5 | δ-1 θ β0.5 | β0.5 |
| Masson Wavelength | λg | 1.1886 × 10-33 | L | θ-1 | δ θ-1 | 1 |
| Planck Length | LPl | 1.6160 × 10-35 | L | (2πθ)-1 β-0.5 | δ (2πθ)-1 β-0.5 | (2π)-1 β-0.5 |
| Virtual Mas. Lifetime | tg | 3.9649 × 10-42 | T | θ-1 | δ θ-1 | 1 |
| Planck Time | TPl | 5.3906 × 10-44 | T | (2πθ)-1 β-0.5 | δ (2πθ)-1 β-0.5 | (2π)-1 β-0.5 |
| Speed of Light | c | 2.9979 × 108 | LT-1 | 1 | 1 | 1 |
| Planck | h | 6.6261 × 10-34 | ML2T-1 | 1 | 1 | 1 |
| Boltzmann's | k | 1.3807 × 10-23 | MK-1L2T-2 | 1 | 1 | 1 |
| Permittivity | ε0 | 8.8542 × 10-12 | M-1Q2L-3T2 | 2-1 β | 2-1 β | 2-1 β |
| Permeability | µ0 | 1.2566 × 10-6 | MQ-2L | 2 β-1 | 2 β-1 | 2 β-1 |
| First Radiation | c1 | 3.7418 × 10-16 | ML4T-3 | 2 π | 2 π | 2 π |
| Second Radiation | c2 | 1.4388 × 10-2 | KL | 1 | 1 | 1 |
| Orbit. Ang. Momen. | Le | 1.0546 × 10-34 | ML2T-1 | (2 π)-1 | (2 π)-1 | (2 π)-1 |
| Spin Ang. Momen. | Ls | 5.2729 × 10-35 | ML2T-1 | (4 π)-1 | (4 π)-1 | (4 π)-1 |
| Zeeman Splitting | Zs | 4.6686 × 10 | M-1QL-1 | (4 π)-1 | (4 π)-1 | (4 π)-1 |
| Bohr Magneton | µB | 9.2740 × 10-24 | QL2T-1 | (4 π)-1 | δ (4 π)-1 | θ (4 π)-1 |
| Nuclear Magneton | µN | 5.0508 × 10-27 | QL2T-1 | (4 π δ)-1 | (4 π)-1 | θ (4 π δ)-1 |
| Electrical Potential | Ve | 5.1100 × 105 | MQ-1L2T-2 | 1 | δ-1 | θ-1 |
| Electrical Current | ie | 1.9796 × 101 | QT-1 | 1 | δ-1 | θ-1 |
| Electrical Resistance | Re | 2.5813 × 104 | MQ-2L2T-1 | 1 | 1 | 1 |
| Electrical Flux | Φee | 1.2398 × 10-6 | MQ-1L3T-2 | 1 | 1 | 1 |
| Magnetic Flux | Φme | 4.1357 × 10-15 | MQ-1L2T-1 | 1 | 1 | 1 |
| Stefan-Boltzmann | σ | 5.6705 × 10-8 | MK-4T-3 | 2 π5 15-1 | 2 π5 15-1 | 2 π5 15-1 |
| Bohr Radius | a0 | 5.2918 × 10-11 | L | β (2 π)-1 | δ β (2 π)-1 | θ β (2 π)-1 |
| Rydberg Energy | ER | 2.1799 × 10-18 | ML2T-2 | (2 β2)-1 | (2 δ β2)-1 | (2 θ β2)-1 |
| Rydberg | Rî | 1.0974 × 107 | L-1 | (2 β2)-1 | (2 δ β2)-1 | (2 θ β2)-1 |
| Rydberg Frequency | ƒR | 3.2899 × 1015 | T-1 | (2 β2)-1 | (2 δ β2)-1 | (2 θ β2)-1 |
| Schwartzschild Radius | r0g | 2.7610 × 10-36 | L | (π β θ)-1 | δ (π β θ)-1 | (π β)-1 |
| Gravitation | G | 6.6726 × 10-11 | M-1L3T-2 | (2 π β θ2)-1 | δ2 (2 π β θ2)-1 | (2 π β)-1 |
Excluding the basic quantum attributes, the FUPCONs in the above table are based upon the electron except for the following ones:
FUPCON Basis FUPCON
Protonic Nuclear Magneton µN
Massonic Schwarschild masson radius r0g
Massonic Newton's gravitational constant G
An interesting comparison is that between the SE value of the Bohr hydrogen-atom radius, a0, and the SG value of the Schwarschild masson radius, r0g, as follows:
[(β) (2 π)-1] as compared to
[(π β)-1]
and we see that the fine-structure constant, β, occurs in both.
You can convert the value of a FUPCON from one system of unit measures to another by using the appropriate conversion factor selected from the following table depending upon the FUPCON's basis and the original and new systems of unit measures.
| FUPCON
Basis |
MA KB LC TD | System of Unit Measures | ||
| (A+B)-(C+D) | SE | SP | SG | |
| Electronic | 1 | 1 | δ-1 | θ-1 |
| 0 | 1 | 1 or δ0 | 1 or θ0 | |
| -1 | 1 | δ | θ | |
| Protonic | 1 | δ | 1 | δ·θ-1 |
| 0 | 1 or δ0 | 1 | 1 or δ0·θ0 | |
| -1 | δ-1 | 1 | δ-1·θ | |
| Massonic | 1 | θ | δ-1·θ | 1 |
| 0 | 1 or θ0 | 1 or δ0·θ0 | 1 | |
| -1 | θ-1 | δ·θ-1 | 1 | |
| -2 | θ-2 | δ2·θ-2 | 1 | |
In an example of using the table, we convert the SE value of the nuclear magneton, µN, to the SP value, as follows:
1. The nuclear magneton, µN, is a protonic-based FUPCON; therefore, we use one of the three-middle rows of the table.
2. The dimensions of µN are QL2T-1. Using the second column of the table as a guide, we determine that (A + B) - (C + D) = (0 + 0) - [2 + (-1)] = -1; therefore, we use the last row of the Protonic section of the table.
3. The value of the SE factor is (δ-1), and that of the SP factor is 1. The value of the starting factor (SE) must be 1. We multiply both factors by δ to rationalize the SE and SP factors to values of 1 and δ, respectively.
4. We multiply the SE value of µN by the new SP factor of δ to obtain the SP value of µN.
5. To confirm the validity of the conversion process, we convert both the SE and SP values of µN to SI values.
µNe = (4 π δ)-1 qe·λe2·te-1 = (4 π δ)-1 (1.6 × 10-19 C) ×
(2.4 × 10-12 m)2 (8.1 × 10-21 s)-1 =
5.1 × 10-27 A·m2 (232
µNp = (4 π)-1 qp·λp2·tp-1 = (4 π)-1 (1.6 × 10-19 C) ×
(1.3 × 10-15 m)2 (4.4 × 10-24 s)-1 =
5.1 × 10-27 A·m2 (233
The results of the two calculations are equal to each other and to the correct value.
A second example is to convert the SG value of Newton's gravitational constant, G, to the SE value, as follows:
1. Newton's gravitational constant, G, is a massonic-based FUPCON; therefore, we use one of the four-bottom rows of the table.
2. The dimensions of G are M-1L3T-2. Using the second column of the table as a guide, we determine that (A + B) - (C + D) = (-1 + 0) - [3 + (-2)] = -2; therefore, we use the last row of the table.
3. The value of the original SE factor is already 1; therefore, we need not rationalize the values of the two factors.
4. We multiply the SG value of G by the SE factor of θ-2 to obtain the SE value of G.
5. To confirm the validity of the conversion process, we convert both the SG and SE values of G to SI values, as follows:
Gg = (2 π β)-1 mg-1·λg3·tg-2 = (2 π β)-1 (1.9 × 10-9 kg)-1 ×
(1.2 × 10-33 m)3 (4.0 × 10-42 s)-2 =
6.7 × 10-11 kg-1·m2·s-2 (234
Ge = (2 π β θ2)-1 me-1·λe3·te-2 = (2 π β θ2)-1 (9.1 × 10-31 kg)-1 ×
(2.4 × 10-12 m)3 (8.1 × 10-21 s)-2 =
6.7 × 10-11 kg-1·m2·s-2 (235
The results of the two calculations are equal to each other and to the correct value.
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