# Constants of Nature

Every unit of measurement (knot, curie, fortnight, calorie, kilometer, volt, bushel, parsec, milligram, light year, mach, astronomical unit, pascal, dalton, slug, kilohertz, ohm, carat, psi, newton, decade, candle, pound, weber, fathom, dyne, furlong, watt, township, liter, tesla, kilogram, joule, decibel, galileo, ton, farad, second, coulomb, degree Celsius, gallon, femtogray, ampere, btu, millibar, electron-volt, horsepower, foot, gauss, picohenry, Kelvin, lux, erg, hour, langley, acre, attopoise, stokes, etc.), can be reduced to an expression of length, mass, time, charge, temperature, or a combination of these five expressions. In a quantized metric each of these five fundamental expressions have natural limits. Quantization specifically dictates a discrete minimum unit of length and time, and discrete maximum units of mass, charge, and temperature in association with those minimum values. According to quantum mechanics the 5 discrete parameters encoded within Nature are:

 Name of Natural Unit Symbol Value (arbitrary units used today) Value (natural units) Planck length lP 1.616199(97) × 10-35 m 1 Planck mass mP 2.17651(13) × 10-8 kg 1 Planck time tP 5.39106(32) × 10-44 s 1 Planck charge qP 1.875545946(41) × 10-18 C 1 Planck temperature TP 1.416833(85) × 1032 K 1

Quantization also imposes minimum and maximum limits for spacetime curvature. The ratio of a circle’s circumference to its diameter can be used to geometrically represent those limits. In flat spacetime (zero curvature) that ratio is equal to π. In regions with nonzero curvature (e.g.centered around a black hole), the numeric value of that ratio decreases because the circle’s diameter proportionately increases. If space is quantized, it follows that the diameter of a circle with a finite circumference cannot be infinite (the amount of space inside a finite black hole cannot be infinite). In general, the cutoff provided by quantization means that the minimum value for the ratio of a circle’s circumference to its diameter must be greater than zero. Therefore, a circle placed in a region of maximum curvature must have a circumference to diameter ratio that is greater than zero, but less than π. Qst represents the exact minimum value of that ratio by the Cyrillic letter ж. It is interpreted to be a geometric descriptor of spacetime’s maximum state of curvature, and it can also be expressed as the ratio of an electron’s charge to the quantum charge.

The value of this ratio is well established, nevertheless an attempt to formally and independently derive its numeric value from the axioms of a quantized geometry is underway. The goal is to show that this number reflects the maximum limit of curvature imposed by quantization. To that end, supporters of qst are investigating variations of the sequential packing, or space-filling, problem (see the work of by Golomb, Dickman, and Rényi), while others are attempting to depict the interior structure of black holes, according to the rules of the axiomatic system, as a way to geometrically represent this limit of curvature. Updates will be posted as these calculations progress.

We are motivated by the recognition that by combining one particular number ( 0.085424543135(14) ), to π and the five Planck constants, we are able to non-arbitrarily reproduce the constants of Nature. If  this numeric value can be derived from our axioms, then the minimum and maximum states of spacetime curvature will be represented by the geometric, dimensionless numbers:

 Pi π 3.141592653589… Je ж 0.085424543135(14)

By linking this value of ж to our axiomatic set we will be able to show that the constants of Nature are derivatives of its natural geometry. The parameters that encode that geometry ( lP, mP, tP, qP, TP , π, ж,) author the constants of Nature in the following manner.

 Name of Constant Symbol Value (arbitrary units used today) Value (natural units) speed of light c 2.99792458 × 108 m/s lP  / tP Planck’s constant ħ 1.054571726(47) × 10-34 m2 kg/s lP2 mP  / tP gravitational constant G 6.67384(80) × 10-11 m3/kg s2 lP3 / mP tP2 fine-structure constant α 7.2973525698(24) × 10-3 ж2 elementary charge e 1.602176565(35) × 10-19 C ж qP Boltzmann constant k 1.3806488(13) × 10-23 m2 kg/s2 K lP2 mP  / tP2 TP magnetic constant μ0 1.25663706143592… × 10-6 m kg/C2 4π lP mP   / qP2 electric constant ε0 8.854187817… × 10-12 s2 C2/m3 kg tP2 qP2 / 4π lP3 mP Coulomb’s constant κ 8.98755178736821… × 109 m3 kg/s2 C2 lP3 mP  / tP2 qP2 Stefan-Boltzmann constant σ 5.670373(21) × 10-8 kg/s3 K4 π2 mP  / 60 tP3 TP4 von Klitzing constant RK 2.58128074434(84) × 104 m2 kg/s C2 2 π lP2 mP   / ж2 tP qP2 Josephson constant KJ 4.83597870(11) × 1014 s C/m2 kg ж tP qP   / π lP2 mP magnetic flux constant Φ0 2.067833758(46) × 10-15 m2 kg/s C π lP2 mP   / ж tP qP characteristic impedance Z0 3.7673031346177… × 102 m2 kg/s C2 4π lP2 mp  / tP qP2 conductance quantum G0 7.7480917346(25) × 10-5 s C2/m2 kg ж2 tP qP2 / π lP2 mP quantized Hall conductance HC 3.87404614(17) × 10-5 C2/m2 kg ж2 tP qP2 / 2π lP2 mP first radiation constant c1 3.74177153(17) × 10-16m4 kg/s3 4 π2 lP4 mP   / tP3 spectral radiance constant c1L 1.191042869(53) × 10-16 m4 kg/s3 4π lP4 mP   / tP3 second radiation constant c2 1.4387770(13) × 10-2 m K 2π lP TP molar gas constant* R 8.3144621(75) m2 kg mol/s2 K lP2 mP NA  / tP2 TP Faraday constant F 9.64853365(21) × 104 C/mol ж NA qP classical electron radius re 2.8179403267(27) × 10-15 m ж2 lP mP  / m– Compton wavelength λC 2.4263102389(16) × 10-12 m 2π lP mP   / m– Bohr radius a0 5.2917721092(17) × 10-11 m lP mP  / ж2 m– Hartree energy Eh 4.35974434(19) × 10-18 m2 kg/s2 ж4 lP2 m–   / tP2 Rydberg constant R∞ 1.0973731568539(55) × 107 1/m ж4 m–   / 4π lP mP Bohr magneton μB 9.27400968(20) × 10-24 m2 C/s ж lP2 mP qP   / 2 tP m– nuclear magneton μN 5.05078353(11) × 10-27 m2 C/s ж lP2 mP qP   / 2 tP m+ Compton angular frequency ωC 7.763441 × 1020 1/s m–  / tP mP Schwinger magnetic induction Smi 4.419 × 109 kg/s C m–2  / ж mP tP qP gravitational coupling αG 1.7518(21) × 10-45 m–2  / mP2

That’s 31 constants of Nature determined

by the quantized geometry of spacetime!

*The remaining constants also depend on Avogadro’s number, the electron mass, or the proton mass. Avogadro’s number (NA), also known as Loschmidt’s number (NL), is used in the the molar gas constant and the Faraday constant. This number is the result of somewhat arbitrary historical conditions wherein the number of atoms in a volume (whose scale was defined by the popular arbitrary system at the time and the personal choice of atom) was chosen as the definition. Avogadro’s number NA is equal to 6.02214179(30) × 1023/mol. The mass of the electron (m) is equal to 9.10938215(45) × 10-31 kg, and the mass of the proton (m+) is equal to 1.672621637(83) × 10-27 kg.