1. …understanding momentum in spacetime
Four-Momentum
…understanding momentum in spacetime
R9T.1, R9T.5

2. Newtonian Ideas break down…
Conservation of (Newtonian) momentum becomes frame-dependent
This violates the first principle of relativity
Home frame: mass m1 moves v1 = 3/5; m2 (= 2m1) moves v2 = 0
Collision is elastic (e = 1). What is the final velocity of each piece. (remember what e is!)
Rocket frame: let b = 3/5. Is momentum conserved as seen from the rocket frame?

3. Four-Momentum
Motion through spacetime

4. 4-momentum (column vector)

5. Four-Vectors
Let A be a 4-vector = [At,Ax,AyAz]
The metric is:

6. 4-momentum transforms via the Lorentz Transformations
Show that