Re: model for early cosmological symmetry breaking as a 3d surface
- To: mathgroup at smc.vnet.net
- Subject: [mg102006] Re: model for early cosmological symmetry breaking as a 3d surface
- From: David Reiss <dbreiss at gmail.com>
- Date: Sun, 26 Jul 2009 03:55:35 -0400 (EDT)
- References: <h4ef00$ss9$1@smc.vnet.net>
I assume you meant SU(8)->U(1)*SU(2)*SU(5)~ SO(8) --david On Jul 25, 4:16 am, Roger Bagula <roger.bag... at gmail.com> wrote: > http://www.flickr.com/photos/fractalmusic/3743178759/ > > This model is a Lorentzian model for the SO(8) > that existed after SU(6) > broken symmetry gave: > SU(6)->U(1)*SU(2)*SU(5)~ SO(8) > where the constant e broke into G gravity constant ~10^-8 ( a force > that attracts) > and Gstar tachyon constant ~10^-12 ( a force that repels). > Some where after Pi solidified at the present valure at t=10^(-11) > second. > The first inflationary era of cosmology. > The second era is the standard model breaking: > SU(5)->U(1)*SU(2)*SU(3) > > What I did was put in likely values and > plot as a 4d Clifford torus projection. > The x and y are each representations of three spacial dimensions. > The resulting surface looks like a bent pseudosphere. > Mathematica: > Clear[x, y, c, tau, t, vg, vp, gamma, n] > (* basic velocity and cordinates as cyclic on radius one*) > x = Cos[t]; > y = Cosh[tau]; > vg = 1/Sqrt[9]; > gamma = vg2/c2; > c = 1; > > (* Lorentz: negative curvature: vg=group velociry <c*) > x1 = (x - vg*t)/Sqrt[1 - vg2/c2]; > t1 = (t - vg*x/c2)/Sqrt[1 - vg2/c2]; > FullSimplify[x12 - c2*t12] > > (* anti - Lorentz: positive curvature : vp=phase velocity>c*) > y1 = (y + vp*tau)/Sqrt[1 + vp2/c2]; > tau1 = (tau - vp*y/c2)/Sqrt[1 + vp2/c2]; > FullSimplify[y12 + c2*tau12] > > (* tachyonic phase velocity*) > vp = c2/vg - ((1 - gamma)/(1 + gamma))*vg > (* Lorentz 4d Clifford torus projection*) > g0 = ParametricPlot3D[{x1/(Sqrt[3] - c*tau1), > y1/(Sqrt[3] - c*tau1), c*t1/(Sqrt[3] - c* > tau1), {EdgeForm[]}}, {t, -Pi, Pi}, {tau, -Pi, Pi}, Boxed -> False= , > Axes -> False] > g1 = ParametricPlot3D[{-x1/(Sqrt[ > 3] - c*tau1), y1/( > Sqrt[3] - c*tau1), -1 - c*t1/(Sqrt[3] - c*tau1), {Edge= Form > []}}, { > t, -Pi, Pi}, {tau, -Pi, Pi}, Boxed -> False, Axes -> False= ] > Show[{g0, g1}, ViewPoint -> {-0.047, 3.170, 1.184}] > Show[{g0, g1}, ViewPoint -> {-1.314, 2.830, 1.310}] > > I'd like to put in a plug for the Mathematica programming yahoo group:htt= p://tech.groups.yahoo.com/group/Active_Mathematica/