# 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 l P 1.616199 (97) × 10 -35 m 1 Planck mass m P 2.17651 (13) × 10 -8 kg 1 Planck time t P 5.39106(32) × 10 -44 s 1 Planck charge qP 1.875545946(41) × 10 -18 C 1 Planck temperature T P 1.416833(85) × 10 32 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 ( l P, m P, t P, q P, T P , π, ж,) author the constants of Nature in the following manner.

 Name of Constant Symbol Value ( arbitr ary units used today ) Value ( natu ral units ) speed of light c 2.99792458 × 10 8 m/s lP  / tP Planck’s constant ħ 1.054571726(47) × 10 -34 m 2 kg/s l P 2 m P  / t P gravitational constant G 6.67384(80) × 10 -11 m 3 /kg s 2 l P 3 / m P t P 2 fine-structure constant α 7.2973525698(24) × 10 -3 ж 2 elementary charge e 1.602176565(35) × 10 -19 C ж q P Boltzmann constant k 1.3806488(13) × 10 -23 m 2 kg/s 2 K l P 2 m P  / t P 2 T P magnetic constant μ 0 1.25663706143592… × 10 -6 m kg/C 2 4π l P m P   / q P 2 electric constant ε 0 8.854187817… × 10 -12 s 2 C 2 /m 3 kg t P 2 q P 2 / 4π l P 3 m P Coulomb’s constant κ 8.98755178736821… × 10 9 m 3 kg/s 2 C 2 l P 3 m P  / t P 2 q P 2 Stefan-Boltzmann constant σ 5.670373(21) × 10 -8 kg/s 3 K 4 π 2 m P  / 60 t P 3 T P 4 von Klitzing constant R K 2.58128074434(84) × 10 4 m 2 kg/s C 2 2 π l P2 m P   / ж 2 t P q P 2 Josephson constant K J 4.83597870(11) × 10 14 s C/m 2 kg ж t P q P   / π l P2 m P magnetic flux constant Φ 0 2.067833758(46) × 10 -15 m 2 kg/s C π l P 2 m P   / ж t P q P characteristic impedance Z0 3.7673031346177… × 10 2 m 2 kg/s C 2 4π l P 2 m p  / t P q P 2 conductance quantum G 0 7.7480917346(25) × 10 -5 s C 2 /m 2 kg ж 2 t P q P 2 / π l P 2 m P quantized Hall conductance H C 3.87404614(17) × 10 -5 C 2 /m 2 kg ж 2 tP q P 2 / 2π l P 2 m P first radiation constant c 1 3.74177153(17) × 10 -16 m 4 kg/s 3 4 π 2 l P 4 m P   / t P 3 spectral radiance constant c1L 1.191042869(53) × 10 -16 m 4 kg/s 3 4π l P 4 m P   / t P 3 second radiation constant c 2 1.4387770(13) × 10 -2 m K 2π l P T P molar gas constant* R 8.3144621(75) m 2 kg mol/s 2 K l P 2 m P N A  / t P 2 T P Faraday constant F 9.64853365(21) × 10 4 C/mol ж N A q P classical electron radius r e 2.8179403267(27) × 10 -15 m ж 2 l P m P  / m – Compton wavelength λ C 2.4263102389(16) × 10 -12 m 2π l P m P   / m – Bohr radius a 0 5.2917721092(17) × 10 -11 m l P m P  / ж 2 m – Hartree energy E h 4.35974434(19) × 10 -18 m 2 kg/s 2 ж 4 l P 2 m –   / t P 2 Rydberg constant R ∞ 1.0973731568539(55) × 10 7 1/m ж 4 m –   / 4π l P m P Bohr magneton μ B 9.27400968(20) × 10 -24 m 2 C/s ж l P 2 m P q P   / 2 t P m – nuclear magneton μ N 5.05078353(11) × 10 -27 m 2 C/s ж l P 2 m P q P   / 2 t P m + Compton angular frequency ω C 7.763441 × 10 20 1/s m –  / t P m P Schwinger magnetic induction S mi 4.419 × 10 9 kg/s C m – 2  / ж m P t P q P gravitational coupling α G 1.7518(21) × 10 -45 m – 2  / m P 2

That’s  31  constants of Nature   determined

b y the quantized geometry of spacetime!

*The remaining constants also depend on Avogadro’s number, the electron mass, or the proton mass. Avogadro’s number ( N A ), also known as Loschmidt’s number ( N L ), 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 N A is equal to 6.02214179(30) × 10 23 /mol. The mass of the electron ( m ) is equal to 9.10938215(45) × 10 -31 kg, and t he mass of the proton ( m + ) is equal to 1.672621637(83) × 10 -27  k g.