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Author Topic: Hadron Mass Spectrum From First Principles Using Fractal Paradigm  (Read 677 times)
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rloldershaw
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Posts: 63


« on: December 25, 2009, 05:52:09 AM »

On the morning of 12/21 I was playing around with the basic
Kerr relation between M, J and G:


Kerr solution: J = aGM^2/c


One can rearrange terms and get this simple equation.


m(n) = [n]^1/2 [constant], i.e.,  sqrt[n] [constant]


where: a = 1/n   and
constant = corrected Planck mass = 674 Mev


The [constant] = the corrected Planck mass [= 674 Mev],
 See: http://arxiv.org/ftp/astro-ph/papers/0701/0701006.pdf
for a derivation of this constant using a discrete fractal paradigm.


--------------------------------------------------------------------
Retrodictive Test


  -n----[n]^1/2[constant]----Empirical mass---Agreement


  1/36------112.3------muon 105.7------------94.0 %
  1/25------134.8------pion  134.98-----------99.9 %
  1/2--------476.6-----kaon  497.7-------------95.8 %
  3/4--------583.7-----eta   547.8--------------93.4%
  1----------674---------Planck mass--------  -----
  2----------953.2-------proton 938-------------98.3 %
  2----------953.2-------neutron939.2?--------98.5%
  2----------953.2-------eta'    958--------------99.5 %
  3--------1167.4-------Lambda 1115.7------95.4 %
  3--------1167.4-------Sigma  1192----------97.9 %
  4--------1348.0-------Xi    1314.8------------97.5 %
  5--------1507.1-------N    ~ 1450------------96.1 %
  6--------1651---------Omega  1672.5-------98.7 %
  7--------1783---------TAU    1784.1---------99.95%
  8--------1906.3-------D     1864.-------------97.8 %
  10------2131.4-------D(s)  2112.2-----------99.1 %
  12------2334.8-------Lam(c)2284.9---------97.8%


Well, that is the 16 most common and stable of the
particles observed, with the exception of the electron
which has n = 1/(1319)^2 and I want to study that a
bit more.  Maybe only a full Kerr-Newman solution will suffice here.


My argument is that this high degree of ordering
demands an explanation. The fact that it was achieved
with the admittedly very approximate Kerr solution
makes things even more interesting. The fact that
Discrete Scale Relativity is definitively required to
determine the crucial value of the corrected Planck
mass should be fully appreciated.


So we can perhaps understand Regge trajectories and
the particle mass spectrum using only 4-d General Relativity + classical EM
+ Discrete Scale Relativity.  No need of extra dimensions, strings, or other epicycles.


Happy Winter Solstice [33rd anniversary of DSR]
Robert L. Oldershaw -
www.amherst.edu/~rloldershaw


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