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 must have a nat­ural quan­tized value (quan­ti­za­tion dic­tates a dis­crete min­imum unit of length and time, and a dis­crete max­imum unit of mass, charge, and tem­per­a­ture asso­ci­ated with those min­imum values). According to quantum mechanics there are 5 dis­crete para­me­ters encoded by Nature. These values are:

Name of Natural Unit Symbol Value (arbi­trary units used today) Value (nat­ural units)
Planck length lP 1.616252(81) × 10-35 m 1
Planck mass mP 2.17644(11) × 10-8 kg 1
Planck time tP 5.39124(27) × 10-44 s 1
Planck charge qP 1.875545870(47) × 10-18 C 1
Planck tem­per­a­ture TP 1.416785(71) × 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. But in regions with nonzero cur­va­ture (e.g.centered around a black hole), the ratio decreases because the circle’s diam­eter pro­por­tion­ately increases. If space is quan­tized, then 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.

An attempt to for­mally con­nect a numeric value of this max­imum limit of cur­va­ture to the geom­etry we have sup­posed is underway. Supporters of qst are inves­ti­gating vari­a­tions of the sequen­tial packing, or space-filling, problem (see the work of by Golomb, Dickman, and Rényi) in an attempt to find an exact numeric expres­sion of this con­di­tion. Others are attempting to depict the inte­rior struc­ture of black holes, according to the rules of this axiomatic system, hoping to extract a geo­metric rep­re­sen­ta­tion of the limits of cur­va­ture encoded by those rules. Updates will be posted as these cal­cu­la­tions progress.

In the mean time, we have rec­og­nized that by com­bining one par­tic­ular number ( 0.302822121(11) ), to π and the five Planck con­stants, we are able to non-arbitrarily repro­duce the con­stants of Nature. For this reason we hypoth­e­size that this numeric value can be derived from our axioms. If it can, then the min­imum and max­imum states of space­time cur­va­ture will be rep­re­sented by the geo­metric, dimen­sion­less numbers:

 

Pi π 3.141592653589…
Je

ж

0.302822121(11)

 

By linking this value of ж to our axiomatic set we will be able to show that the con­stants of Nature are deriv­a­tives of this 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 1.054571628(53) × 10-34 m2 kg/s lP2 mP /tP
grav­i­ta­tional constant G 6.67428(67) × 10-11 m3/kg s2 lP3/mP tP2
fine-structure con­stant α 7.2973525376(50) × 10-3 ж2/4π
ele­men­tary charge e 1.602176487(40) × 10-19 C ж qP /√(4π)
Boltzmann con­stant k 1.3806504(24) × 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 /4π tP2 qP2
Stefan-Boltzmann con­stant σ 5.670400(40) × 10-8 kg/s3 K4 π2 mP /60 tP3 TP4
von Klitzing constant RK 2.5812807557(18) × 104 m2 kg/s C2 8 π2 lP2 mP/ж2 tP qP2
Josephson con­stant
KJ 4.83597891(12) × 1014 s C/m2 kg ж tP qP /π √(4π)  lP2 mP
mag­netic flux constant Φ0 2.067833667(52) × 10-15 m2 kg/s C π √(4π) lP2 mP/ж tP qP
char­ac­ter­istic impedance Z0 3.7673031346177… × 102 m2 kg/s C2 4π lP2 mp /tP qP2
con­duc­tance quantum G0 7.748091733(26) × 10-5 s C2/m2 kg ж2 tP qP2/4 π2 lP2 mP
quan­tized Hall conductance HC 3.87404614(17) × 10-5 C2/m2 kg ж2 qP2 / 8 π2 lP2 mP
first radi­a­tion constant c1 3.74177118(19) × 10-16m4 kg/s3 4 π2 lP4 mP/tP3
spec­tral radi­ance constant c1L 1.19104282(20) × 10-16 m4 kg/s3 4π lP4 mP/tP3
second radi­a­tion constant c2 1.4387752(25) × 10-2 m K 2π lP TP
molar gas constant* R 8.314472(15) m2 kg mol/s2 K lP2 mP NA /tP2 TP
Faraday con­stant F 9.64853383(83) × 104 C/mol ж NA qP / √(4π)
clas­sical elec­tron radius re 2.8179402894(58) × 10-15 m ж2 lP mP /4π melec­tron
Compton wave­length λC 2.42631023816 × 10-12 m 2π lP mP/melec­tron
Bohr radius a0 5.291772108(18) × 10-11 m 4π lP mP/ж2 melec­tron
Hartree energy Eh 4.35974417(75) × 10-18 m2 kg/s2 ж2 lP2 melec­tron/(4π)2 tP2
Rydberg con­stant R 1.0973731568525(73) × 107 1/m ж4 melec­tron/(4π)3 lP mP
Bohr mag­neton μB 9.27400915(23) × 10-24 m2 C/s ж lP2 mP qP /4√(π) tP melec­tron
nuclear mag­neton μN 5.05078343(43) × 10-27 m2 C/s ж2 lP2 mP qP /4√(π) tP mproton
Compton angular frequency ωC 7.763441 × 1020 1/s melec­tron /tP mP
Schwinger mag­netic induction Smi 4.419 × 109 kg/s C √(4π) melec­tron2/mP tP qP
grav­i­ta­tional coupling αG 1.7518 × 10-45 melec­tron2/mP2

 

That’s31con­stants of Nature that are

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 (melec­tron) is equal to 9.10938215(45) × 10-31 kg, and the mass of the proton (mproton) is equal to 1.672621637(83) × 10-27kg.