Constants of Nature

All descrip­tors that we use to describe the world around us and the inter­ac­tions within it (Pascals, Newtons, Dynes, etc.) can be reduced to expres­sions of length, mass, time, ampere, and tem­per­a­ture (or com­bi­na­tions of these five expres­sions). Quantizing space­time requires that we have nat­ural quan­tized values for these five expres­sions (one fun­da­mental unit of length, mass, time ampere, and tem­per­a­ture). The five dis­crete para­me­ters that relate these fun­da­mental expres­sions are the Planck para­me­ters. Their values are:

Constants of Nature that are dimen­sion­ally set by this quan­ti­za­tion are:

Constant Name	Symbol	Value (arbi­trary units used today)	Value (nat­ural units)
speed of light	c	2.99792458 × 108 m/s
Planck’s con­stant	ħ	1.05457162853 × 10-34 m2kg/s
grav­i­ta­tional constant	G	6.6742 × 10-11 m3/kg s2
mag­netic constant	μ0	4π × 10-7 m kg/s2 A2
elec­tric constant	ε0	8.854187817… × 10-12 s4 A2/m3 kg
Boltzmann con­stant	K	1.380650524 × 10-23 m2 kg/s2 K
char­ac­ter­istic impedance	Z0	3.76730313461… × 102 m2 kg/s3 A2
molar gas constant*	R	8.31447215 m2 kg mol/s2 K

Two other dimen­sion­less, geo­metric num­bers are part of our quan­tized map. These num­bers reflect the limits of cur­va­ture in that map. The min­imum limit of cur­va­ture can be rep­re­sented as a ratio of a circle’s cir­cum­fer­ence to its diam­eter in regions where the cur­va­ture is zero. This ratio gives us the familiar value of π. However, if we were to center a circle on a black hole we would find that this ratio decreases in value because the diam­eter respec­tively increases. When space is quan­tized the cur­va­ture of space cannot increase indef­i­nitely. There must be a cutoff some­where. Consequently, there must also be a ratio that rep­re­sents that limit of cur­va­ture. We rep­re­sent that limit with a new geo­metric dimen­sion­less number called ж. (A formal deriva­tion of the exact value of this number, out to arbi­trary digits, is underway, but has not yet been com­pleted.) Because ж is defined as a ratio, its value does not depend upon the size of the black hole.

These unit­less markers of the limits of space­time cur­va­ture in a quan­tized geom­etry are:

Combining π and ж, with the 5 quan­tized geo­metric values of quan­ti­za­tion, the fol­lowing con­stants of Nature also jump out of the formalism.

Constant Name	Symbol	Value (arbi­trary units used today)	Value (nat­ural units)
fine-structure con­stant	α	7.297352537 × 10-2
inverse fine-structure constant	α-1	1.37035999694 × 102
ele­men­tary charge	e	1.6021765314 × 10-19 sA
Josephson con­stant	KJ	4.8359787941 × 1014 s2A/m2kg
Faraday con­stant*	F	9.648533883 × 104 sA/mol
mag­netic flux constant	Φ0	2.0678337218 × 10-15 m2kg/s2A
con­duc­tance quantum	G0	7.74809173326 × 10-5 s3A2/m2kg
inverse con­duc­tance quantum	G0-1	1.290640372543 × 104 m2kg/s3A2
von Klitzing constant	RK	2.581280744986 × 104 m2kg/s3A2
Bohr mag­neton	μB	9.2740094980 × 10-24 m2A
nuclear mag­neton	μN	5.0507834343 × 10-27 m2A
Bohr radius	a0	5.291177210818 × 10-11 m
Hartree energy	Eh	4.3597441775 × 10-18 m2kg/s2
Compton wave­length	λC	2.42631023816 × 10-12 m
Stefan-Boltzmann con­stant	σ	5.67040040 × 10-8 kg/s3K4
Rydberg con­stant	R∞	1.097373156852573 × 107 1/m
first radi­a­tion constant	c1	3.7417713864 × 10-16 m4kg/s3
spec­tral radi­ance constant	c1L	1.1910428220 × 10-16 m4kg/s3
second radi­a­tion constant	c2	1.438775225 × 10-2 mK

*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 6.022141510 × 10²³/mol.