franznietzsche
Dec16-03, 07:53 PM
Here's a few kickers for those of you who don't know a lot about the mathematics of relativity:
The locus of all points equidistant from the origin is a four dimensional hyberbola given by:
d^2=(y_1-x_1)^2+(y_2-x_2)^2+(y_3-x_3)^2-c^2(y_4-x_4)^2
where c is the speed of light. Also the cross section of this perpendicular to the time axis (x_4) is a sphere, the euclidean locus of equidistant points.
the reason the -c^2 is in the equation is the Minkowski metric which also determines the lorentz transformation that makes inertia increase as velocity increases etc. Hope someone else finds this tidbit entertaining.
The locus of all points equidistant from the origin is a four dimensional hyberbola given by:
d^2=(y_1-x_1)^2+(y_2-x_2)^2+(y_3-x_3)^2-c^2(y_4-x_4)^2
where c is the speed of light. Also the cross section of this perpendicular to the time axis (x_4) is a sphere, the euclidean locus of equidistant points.
the reason the -c^2 is in the equation is the Minkowski metric which also determines the lorentz transformation that makes inertia increase as velocity increases etc. Hope someone else finds this tidbit entertaining.