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

 

 

 

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