Question

Show explicitly that two successive Lorentz transformations in the same direction (with velocity v_1 and v_2, respectively) are equivalent to a single Lorentz transformation with a velocity v = (v_1 + v_2)/(1 + (v_1v_2)/c^2) Compare with the relativistic velocity-addition law.

Name: show explicitly that two successive lorentz transformations in the same direction with velocity v1 and v2 respectively are equivalent to a single lorentz transformation with a velocity v v1 v21 v
Uploaded: 2023-05-24T11:31:00-08:00
Duration: 5 min 17 s
Channel: Sam Stansfield
Description: show explicitly that two successive lorentz transformations in the same direction with velocity v1 and v2 respectively are equivalent to a single lorentz transformation with a velocity v v1 v21 v

          Show explicitly that two successive Lorentz transformations in the same direction (with velocity v_1 and v_2, respectively) are
equivalent to a single Lorentz transformation with a velocity

v = (v_1 + v_2)/(1 + (v_1v_2)/c^2)

Compare with the relativistic velocity-addition law.

Added by Tee S.

Mechanics Berkeley Physics

Charles Kittel, Walter D. Knight, Malvin… 2nd Edition

Chapter 12

Instant Answer

Solved by Expert Sam Stansfield

05/24/2023

Step 1

First, let's recall the Lorentz transformation equations for a boost in the x-direction: x' = γ(x - vt) t' = γ(t - vx/c^2) where γ = 1 / sqrt(1 - v^2/c^2) is the Lorentz factor. Show more…

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Show explicitly that two successive Lorentz transformations in the same direction (with velocity v_1 and v_2, respectively) are equivalent to a single Lorentz transformation with a velocity v = (v_1 + v_2)/(1 + (v_1v_2)/c^2) Compare with the relativistic velocity-addition law.