Title: Hadron Mass Spectrum From First Principles Using Fractal Paradigm Post by: rloldershaw 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 |