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 ( 0.0854245431(31) ), 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 m / tP
grav­i­ta­tional constant G 6.67384(80) × 10-11 m3/kg s2 lP/ 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 m / 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 qP/ 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 q  / 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 m / tP qP2
con­duc­tance quantum G0 7.7480917346(25) × 10-5 s C2/m2 kg ж2 tP qP/ π lP2 mP
quan­tized Hall conductance HC 3.87404614(17) × 10-5 C2/m2 kg ж2 tqP2 / 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 N / 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.