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 / t P
grav­i­ta­tional constant G 6.67384(80) × 10 -11 m 3 /kg s 2 l P / 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 / 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 / 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   / 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 / 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 / π l P 2 m P
quan­tized Hall conductance H C 3.87404614(17) × 10 -5 C 2 /m 2 kg ж 2 tq 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 / 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.