
Fundamental
constants are some numbers with units that cannot (yet) be calculated from some physical theory,
but must be measured. 


This may have three possible reasons:
 There is presently no theory, and there never will be a theory, that allows us to
calculate fundamental constants. They have the value they have because an act of
one or more gods and/or godesses, or they are purely random (i.e we just happen to live in an universe, where the value
is what we measure. In some other universe, or some other corner of our universe, it will be arbitrarily different).
 There is presently no theory, but some day there will be one. Some fundamental constants will then be calculated and
then are no longer fundamental.
 There already is a theory, or at least a general theoretical framework; we just are not yet smart enough to see the
obvious or to do the numerics. Masses of elementary particles, e.g., might be "fundamental constants" that fall
into this category.



Hotshot physicists have some ideas, which constant might fall into which category. Speculations
along this line are a lot of fun  but of no consequence so far. So I will not dwell
on this. (Of course, you may check for yourself which one of the three possibilities
you are going to embrace and thus get some idea of what kind of person you are). 

Fundamental physical theories usually introduce one new fundamental constant.
Mechanics (including gravitation) needs the gravity constant G, quantum theory has Plancks constant h, statistical
thermodynamics introduces Boltzmanns constant k, the special theory of relativity (or Maxwells theory of electromagnetism
which is really part of the relativity theory) needs the speed of light c. 


New theories sometimes "explain" old constants of nature because they can calculate
them, or replace them by something more fundamental. Boltzmann's constant k, for example, is more fundamental than
the "fundamental" gas constant R, because it relates its number to a fundamental unit of matter (1 particle)
and not to an arbitrary one like 1 mol. 

How many truly fundamental constants are there? Why do they have the values they
have? (Just slight deviations in the values of some constants would make carbon based life impossible; this is where the
socalled "anthropic principle"
comes in). Will we eventually be able, with a "Theory of Everything" (TOE) to calculate all natural constants? 


Nobody knows. We run against the deepest physical questions at this point. 


So let's just look at what we have. Since it is customary to list as natural constants some
quantities that are actually computable from others, we include some of these "constants" here, too (together
with the conversion formula). 
Symbol and formula 
Numerical value 
Magnitude and unit 
Remarks 
Speed of light in vacuum 
c_{0}, c  2.997,924,58 
10^{8}m·s^{–1}  Truly fundamental 
Gravitational constant 
G  6.673 
10^{–11} m^{3}·kg^{–1}·s^{–2} 
Truly fundamental 
Planck's constant 
h  6.626,068,76 
10^{–34}J·s  Truly fundamental 
4.135,6  10^{–15} eV·s 
Elementary charge 
e  1.602,176,462  10^{–19}C 
Truly fundamental ? Maybe not 
Fine structure constant 
a = µ_{0}·c·e^{2}/2h 
7.297,352,533  10^{–3} 
Unitless, maybe more fundamental than others. 
Mass of a electron at rest 
m_{e}  9.109,381,88 
10^{–31} kg 
Not truly fundamental; can be calculated in principle 
0,510 998 902  MeV 
Mass of a proton at rest 
m_{p}  1.672,621,58 
10^{–27} kg 
Not truly fundamental, can be calculated in principle 
1.007,276,466  u 
938.271,998(38)  MeV 
Avogadro constant 
N_{A}  6.022,141,99(47) 
10^{23} mol^{–1} 
Not truly fundamental any more 
Faraday constant 
F = e·N_{ A}  96,485.3415(39) 
C·mol^{–1}  Not truly fundamental any more 
Universal gas constant  R 
8.314,472(15) 
J·mol^{ –1}·K^{–1} 
Not truly fundamental any more 
Boltzmann constant 
k = R/N_{A}  1.380,650,3 
10^{ –23} J·K^{–1} 
Truly fundamental  8.617,269 
10^{–5} eV·K^{–1} 
Magnetic permeability of vacuum 
µ_{0} = 1/e_{0}c^{2} 
12.566,370,614 
10^{–7} V·s·A^{–1}m^{–1} 
Not truly fundamental 
Electric susceptibility of vacuum 
e _{0} = 1/µ_{0}c^{2} 
8.854,187,817 
10^{–12}A·s·V^{–1}m^{–1} 
Not truly fundamental 
Magnetic flux quant 
P = h/2e  2.067,833,636 
10^{–15} Wb 
Smallest possible magnetic flux Not truly fundamental 
