|Jul12-12, 02:31 PM||#1|
I have a probability density which in its rest frame is evenly painted upon a 2-sphere. I need to figure out how that density transforms under a Lorentz boost.
Heuristically, this will consist of boosting the 2-sphere to obtain an ellipsoid of some sort, then doing a parallel projection along the boost axis back onto the sphere.
At least the first part of this, I think, is a fairly standard problem since it is similar to that of calculating the beaming of synchrotron radiation. I was just wondering if anyone knows of a source that works through it so I don't have to do the whole thing from scratch.
|Jul13-12, 10:08 AM||#2|
|Jul13-12, 10:10 AM||#3|
I mean, a spherical shell (the surface of a ball). I need e.g. parametric equations or something for the resulting surface.
|Jul13-12, 02:12 PM||#4|
Do you mean you have some evenly spaced set of points on the shell with associated density magnitude like;
P1 = (x1, y1, z1, density_1)
P2 = (x2, y2, z2, density_2)
P3 = (x3, y3, z3, density_3) etc.
Or do you have a set of “dots” like;
P1 = (x1, y1, z1)
P2 = (x2, y2, z2)
P3 = (x3, y3, z3) etc.
And the density at any area is determined by the number of dots?
Or do you mean something different?
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