 July 27, 2004

A simple mass relation found for the electron

and the other leptons.

The lepton particle family

I think I've made a rather interesting discovery here:  It's well known that electron has two bigger brothers, the muon and the tau lepton. each of the three has its own anti particle. (The electron's anti-particle is the positron)

There are 3 generations of particles in nature. Three generations of leptons, three generations of neutrinos and three generations of quarks. The first generations form almost all of the matter in the universe. The 2nd and 3rd generation particles have limited lifetimes and seem to play a much less important role.

 generation name mass symbol mass value in MeV average    life time 1 electron me 0.51099892 MeV  (+/-0.00000004) > 4.6  10 26   yr 2 muon mμ 105.658369 MeV  (+/-0.000009) 2.197  10 -6    s 3 tau mτ 1776.99000 MeV  (+0.29 -0.26) 290.6  10 -15  s

I've  now found surprisingly simple formulas for the mass ratio's of the three leptons.

The lepton mass ratio formulas found:

You can find the actual formula's in the table below. They are not only very simple but also exact to within less then 0.1% giving us the confidence that we can actually draw some conclusions on them. The simplest formula is surprisingly the one that describes the step from generation three to two:

 ratio from / to formulas found for the logarithm      of the measured mass ratios: precision tau => muon generation 3 to 2 ln ( mτ / mμ )  =     π  -  1/π -  0.029 % muon => electron generation 2 to 1 ln ( mμ / me )  =    2π -  3/π + 0.063 % tau => electron generation 3 to 1 ln ( mτ / me )  =    3π  -  4/π + 0.031 %

Many scientist have been looking for a fourth generation. There is however indirect experimental proof that there are no

more than 3 generations in nature.

Regards, Hans 