Constants
Physical constants in Paludal units (3-4 significant dozenal digits unless exact). "Exact" means fixed by definition; measured values carry the same uncertainty as in SI.
Defining constants (exact)
| Constant | Paludal value | SI value (dec) |
|---|---|---|
| Breath (defines time) | 25/6 SI seconds; today = 7,50E,583,273 caesium periods | 9,192,631,770 Hz caesium |
| Speed of light c | 2 × 10^7 p/bl (2 × 10^8 p/br) | 299,792,458 m/s |
| Planck constant h | 2;13 × 10^-28 li·p²/bl | 6.62607015 × 10^-34 J s |
| Elementary charge e | 1 × 10^-16 os | 1.602176634 × 10^-19 C |
| Boltzmann constant k | 2;07 × 10^-1E op/tep | 1.380649 × 10^-23 J/K |
| Grex number | 1;15 × 10^1X per grex | 6.17235 × 10^23 (Avogadro: 6.022 × 10^23) |
| Luminous efficacy K_cd | 3 × 10^4 lam·sr/vg, for light at 19,042,90X,764,540 per blink | 683 lm/W, at 540 THz |
Derived from them (also exact)
| Constant | Paludal value | SI value (dec) |
|---|---|---|
| Reduced Planck ħ = h/2π | 4;028 × 10^-29 li·p²/bl | 1.054572 × 10^-34 J s |
| Gas constant R = k × grex number | 0;2359E op/(tep·gx) | 8.314 J/(mol K) |
| Faraday constant F = e × grex number | 1;15 × 10^4 os/gx | 96,485 C/mol |
| Stefan-Boltzmann σ | 1;735 × 10^-9 vg/(p²·tep⁴) | 5.670 × 10^-8 W/(m² K⁴) |
| Josephson constant K_J = 2e/h | 10^12 / 2;13 ≈ E;4X56 × 10^11 per (bl·im) | 483,597.848 × 10^9 Hz/V |
| von Klitzing constant R_K = h/e² | 2;13 × 10^4 im/ri | 25,812.807 Ω |
- The von Klitzing constant comes out round because h and e are: it carries h's digits (2;13). Standards labs realise the volt with Josephson junctions and the ohm with the quantum Hall effect, through exactly these two constants, so Paludal's electrical units can be realised directly, without going through SI
Measured
Values from CODATA 2022 CE. The relative uncertainty is a ratio, so it's the same in any units; the Paludal values are rounded to 3-4 dozenal digits.
| Constant | Paludal value | SI value (dec) | Relative uncertainty (dec) |
|---|---|---|---|
| Gravitational constant G | 3;558 × 10^-E p³/(li·bl²) | 6.67430 × 10^-11 m³/(kg s²) | 2.2 × 10^-5 |
| Electron mass | X;21 × 10^-25 li | 9.1093837139 × 10^-31 kg | 3.1 × 10^-10 |
| Proton mass | X;986 × 10^-22 li | 1.67262192595 × 10^-27 kg | 3.1 × 10^-10 |
| Fine-structure constant α (no units) | 1 / E5;0522 | 1 / 137.035999177 | 1.5 × 10^-10 |
| Magnetic constant μ0 | 2;265 × 10^-5 vi/ri² | 1.25663706127 × 10^-6 N/A² | 1.6 × 10^-10 |
| Electric constant ε0 = 1/(μ0 c²) | 1;435 × 10^-X os/(im·p) | 8.8541878188 × 10^-12 F/m | 1.6 × 10^-10 |
- μ0 and ε0 are measured, as in SI since 2019 CE: with h and e fixed, μ0 = 2αh/(e²c), so it carries α's uncertainty. In Paludal the exact factor is short: μ0 = α × 2;13 × 10^-3 vi/ri² (2;13 × 10^-3 is 2R_K/c)
Earth and everyday
| Value | Paludal | SI (dec) |
|---|---|---|
| Standard gravity g_n (exact in SI; Paludal value rounded) | ≈ 0;9926 p/bl² (99;26 p/br²) | 9.80665 m/s² (exact) |
| Standard atmosphere | 5;969 t↑pr | 101,325 Pa |
| Absolute zero | -289;485 °t (exact) | -273.15 °C |
| Water freezes / boils (sea level) | 0 °t / ≈ EE;E9 °t | 0 °C / 99.974 °C |
| Water density | 1;002 li/cu at 4 °C, 0;EEE at 20 °C | 999.97 / 998.2 kg/m³ |
| Speed of sound (20 °C) | ≈ 6X p/bl | 343 m/s |
| Day | 10^5 bl = 10^4 br (exact) | 86,400 s |
| Tropical year | 265;2XX days | 365.2422 days |
| Earth radius (mean) | 1,576 ir | 6,371 km |
| Earth-Moon distance | 7;476 × 10^4 ir | 384,400 km |
| Astronomical unit (Earth-Sun, exact) | 1;7E63 × 10^X p = 1;7E63 × 10^7 ir | 149,597,870,700 m |
| Light from the Sun to Earth | 9E;9 br ≈ X moments | 499.0 s (8 min 19 s) |
| Light from the Moon to Earth | 3;84 bl ≈ 1;3 bt | 1.282 s |
| Light-year (exact) | 5;0X6 × 10^12 p | 9.461 × 10^15 m |
Pure numbers (the same in any base, dozenal digits)
| Number | Dozenal | Decimal |
|---|---|---|
| π | 3;184809493E92 | 3.14159265358979 |
| 2π (radians in a turn) | 6;34941697 | 6.28318531 |
| e | 2;875236069822 | 2.71828182846 |
| √2 (paper ratio) | 1;4E79170X07E8 | 1.41421356237 |
| φ (golden ratio) | 1;74EE6772802X | 1.61803398875 |
- The Faraday constant comes out round because both e and the grex number are round
- g isn't round: c is, and only one of them can be (see Gravity)