
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 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 
4,1356 
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 6503 
10^{–23} J·K^{–1} 
Truly fundamental 
8,617269 
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 
