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

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?

Four-Momentum Motion through spacetime

4-momentum (column vector)

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

4-momentum transforms via the Lorentz Transformations Show that