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Homework 5

# Homework 5 - 1 v v v = 1 2. 1 v1v 2 . vx 1

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Physics 601 Homework 5---Due Friday October 8 1. A standard result in undergraduate relativity is the velocity addition formula: v = v 1 + v 2 1 + v 1 v 2 . This typically obtained by taking the product of two Lorentz transformations and the doing some algebra. A more straightforward way to obtain this use the four velocity: u μ = γ γ v x γ v y γ v z γ = 1 1 v 2 . Suppose I start with a particle moving with velocity v 1 with an associated four‐velocity u 1 μ = γ 1 γ 1 v 1 x γ 1 v 1 y γ 1 v 1 z . Suppose one boosts to a new frame by running to the left (‐ x direction) with a velocity which corresponds to a Lorentz transformation Λ μ ν = γ 2 v 2 γ 2 0 0 v 2 γ 2 γ 2 0 0 0 0 1 0 0 0 0 1 . The four‐velocity in the new frame is u ν = Λ μ ν u 1 ν . a. From the transformed four velocity find v x , v y , v z in the new frame.

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Homework 5 - 1 v v v = 1 2. 1 v1v 2 . vx 1

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