Constants and units in physics
- units form a Lauren ring !
3 basic units
length
time
mass
Planck constant
speed of light
fine structure constant
units
natural units
rest energy of the proton is roughly 1 GeV
\(10^9 eV = 1 GeV \)
constants of standard model
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.
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 Standard Model.