Building a coordinate system on a surface - Part 1
(Or Math of GR part 10 for Calculus nerds)
We saw how to build a Cartesian Coordinate System in real space using rigid rods. Now let's build one made up of curves on a curved surface.
Consider a surface S parametrized as a function of two variables (u,v). Let u and v equal zero and graph the point on the surface as the ORIGIN. Let v = 0, and then graph the curve on the surface S that you get when you let u take on all its possible values. Call this curve the U-axis.
Next, let u = 0, and then graph the curve on the surface S that you get when you let v take on all its possible values. Call this curve the V-axis.
Proving the Relativistic Energy-Momentum relation, the hard way and the easier way.
This adds the proof for the relativistic mass effects from motion, proving that gravity causes it.
