Space Time Coordinate of object <t, x, y, z> = <0, 0, 0, 0>
Velocity of object as Vector <betaX, betaY, betaZ> = <.866, 0 ,0>
Velocity of target reference frame as Vector <betaX, betaY, betaZ> = <-.866, 0 ,0>
Transform velocity of object to the target reference frame using the 4-vector technique.
The Attempt at a Solution
[/B]Following directions from a source on the internet........
Velocity as a 4-vector (tau, vx, vy, vz)
= <1, betaX, betaY, betaZ>
= <1, 0.866, 0.0, 0.0>
magnitude of 4-vector
= Sqrt( 1 + betaX * betaX + betaY * betaY + betaZ * betaZ )
Velocity as a 4-vector normalized (tau, x, y, z)
= <1/magnitude, betaX/magnitude, betaY/magnitude, betaZ/magnitude>
= <0.7559384493044097, 0.6546426970976188, 0.0, 0.0>
Transform the 4-vector where L is the Lorentz Transform populated for the target velocity:
v' = Lv
resulting in v'(tau, x, y, z)
= <2.6454852575216505, 2.6183403845739543, 0.0, 0.0>
??? I should be getting a vx value somewhere around .98c. Totally lost.