Here's a new idea regarding quantum gravity and the reconciliation of GR and QM.
I have now shown that the masses of ~ 20 most common/stable particles [100 Mev to 6500 Mev] can be related by the expresson M = n^1/2 times [correted Planck mass].
Here is a preliminary description; a more detailed discussion is available upon equest.
Kerr solution: J = aGM^2/c
m(n) = [n]^1/2 [constant], i.e., sqrt[n] [constant]
where: a = 1/n and
constant = corrected Planck mass = 674 Mev
-n----n]^1/2[constant]----Empirical mass---Agreement
1/36------112.3------muon 105.7------------94.0 %
1/25------134.8------pi 134.98-----------99.9 %
1/2--------476.6-----k 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 K-N 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.
It appears that subatomic particle masses are eigenvaules of the Kerr-Newman solution of the Einstein-Maxwell equations.
Happy Winter Solstice [33rd anniversary of DSR]
Robert L. Oldershaw
www.amherst.edu/~rloldershaw