Well, 20 is probably not going to do it these days (maybe you were
reading something written before the neutrino oscillation discovery of
the late 1990's). Before the Super Kamiokande experiments in the 1990's
we all thought neutrinos were massless and didn't mix with each other,
and that reduced the number of parameters. Here goes a tabulation of
the parameters of the SM:
masses of electron, muon, and tau leptons (3)
masses of six quarks: up, down, strange, charm, top, bottom (6)
mixing matrix of the down-type quarks, which is parameterized by
four independent angles. To find out more, look up "CKM Matrix" or
"Cabibbo-Kobayashi-Maskawa Mixing Matrix" (4)
The strong coupling constant alpha_s (1)
The fine structure constant alpha_em (1)
The Fermi constant G_F (governs weak decay rates) (1)
The Z boson mass M_Z (1)
The Higgs boson mass (1) (the W mass can be calculated from the other parameters and the theory)
Gravity has a strength parameterized by G_N, Newton's gravitational constant (1).
That's 19. Two constants, the speed of light and Planck's constant, define our units of length and time and energy.
That gets me up to 21. The neutrino masses are another 3, and they
have a mixing matrix just like the down-type quarks for another four
parameters, for a total of 28.
These are the constants of the Standard Model, which is incomplete.
The Standard Model fails to explain dark matter and dark energy. Dark
energy may be parameterizable with just one more constant (Einstein's
famous "cosmological constant") or there may be a much richer set of
things to understand about it.
Dark matter is also a mystery. My favorite candidate for what it is
is supersymmetric partners of ordinary matter. But then all the
supersymmetric partners have masses and mixings and lots of numbers to
describe them, introducing (at one count I can dig up in the Particle
Data Group's review) of 105 new parameters on top of those of the
I think Tom may have over-counted a little. Some of the quantities
listed have units of mass, rather than being simple numbers. If they
were all changed by some factor, and Planck's constant were changed in
the same way, nothing would be physically different. So that would
leave 27. Maybe there is another subtle reduction possible, but that
count is currently about right. Of course the hope is that if enough
other parameters are found, there will be a simplifying theory again
reducing the number to a small set, the same way that the large
collection of properties of different elements reduces to a few of the
parameters of the Standard Model.
(published on 10/22/2007)