       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;
> 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 - c*tau1),
>   y1/(Sqrt - c*tau1), c*t1/(Sqrt - c*
>    tau1), {EdgeForm[]}}, {t, -Pi, Pi}, {tau, -Pi, Pi}, Boxed -> False=
,
> Axes -> False]
> g1 = ParametricPlot3D[{-x1/(Sqrt[
>      3] - c*tau1), y1/(
>          Sqrt - c*tau1), -1 - c*t1/(Sqrt - 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/

```

• Prev by Date: Re: Optimize evaluation of symbolic expressions
• Next by Date: Re: Show doesn't work inside Do loop ?
• Previous by thread: model for early cosmological symmetry breaking as a 3d surface
• Next by thread: Log axis in ListPlot3D