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Q & A: 20 constants of the universe?

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Most recent answer: 10/22/2007
What are the 20 constants of the Univers? Thanks.
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- Mehran
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 Standard Model.


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.

Mike W.
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(published on 10/22/2007)

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