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, electronvolt, 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  q_{P}  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 spacefilling, 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 nonarbitrarily 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 (arbitrary units used today)  Value (natural units) 
speed of light  c  2.99792458 × 10^{8} m/s  l_{P} / t_{P} 
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} 
finestructure 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} 
StefanBoltzmann 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_{P}^{2} 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_{P}^{2} 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  Z_{0}  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} t_{P }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  c_{1L}  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
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 (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 the mass of the proton (m_{+}) is equal to 1.672621637(83) × 10^{27 }kg.