Random Thoughts on the Universe

Sunday, August 20, 2006

The Hitchiker Relation?

The following is a semi-satirical article, and not intended as a serious discovery of a new physical law...

After all of the articles on the Koide relation and the Jacobsen relation, and other lepton mass formulae, we started discussing similiar laws for quark masses, and came upon the most important mass formula yet. As every science-fiction fan knows, the number 42 is the most important number in the Universe (according to the "The
Hitchiker's Guide to the Galaxy" this is the answer to the Ultimate Question of Life, the Universe, and Everything).

We have finally discovered the deep meaning of this!
-Take the mass of the top quark, currently believed to be between 174 GeV and 178 GeV, and divide by 42. The result is between 4.14 GeV and 4.23, the mass of the bottom quark!
-Now divide that by 42 again, and you have 98.6 MeV to 100.7 MeV. This is a middle of the accepted range of the strange quark mass! (which is 80 MeV to 130 MeV)
- Divide by 42 again, and you get 2.3 MeV, which is the middle of the up-quark mass (1.5 to 4 MeV)!

- Now start again with the top quark mass of 178 GeV, but this time divide by 4*42. The result is 1.06 GeV which is slightly below the charm mass (1.15 GeV to 1.35 GeV)!
- Divide that by 4*42 again, and the result is 6.2 MeV. This is in the middle of the allowed down quark mass (4 to 8 MeV)!

Clearly the quarks masses are part of the meaning of life, the Universe and everything!

Now if someone could just find that the charm mass is lower than previously thought...

Wednesday, August 16, 2006

The Jacobsen Relation?

In a previous post, we introduced the mysterious Koide formula in which the masses of the three known leptons satisfy a very simple relation.

Now a new relationship has been discovered and presented by Jacobsen (see the original paper), in which the masses satisfy

m(n) = 3^(n/4) (4 pi)^(1+n) m_e

where m_e is the electon mass, and n is an integer (and ^ represents 'raised to the power of'). Although this formula is not as simple or as beautiful as the Koide formula (and is not even close to having the same accuracy, with mass predictions off by as much as 1% instead of 0.01%), it has one big advantage. This formula expresses the masses in terms of a quantum number n, which provides a strong indication that the heavy leptons are in fact excited quantum states of the electon!

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