Bob is moving at a speed v in the positive x direction relative to Alice. ) Write down the Lorentz transformation from Alice's coordinate sys- tem to Bob's. (You may work in units where c = 1.) ) Alice observes a photon moving in the positive x direction with energy E. What energy does Bob observe the photon as having?
Bob is moving at a speed v in the positive x direction relative to Alice. ) Write down the Lorentz transformation from Alice's coordinate sys- tem to Bob's. (You may work in units where c = 1.) ) Alice observes a photon moving in the positive x direction with energy E. What energy does Bob observe the photon as having?
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Transcribed Image Text:6. Bob is moving at a speed v in the positive x direction relative to Alice.
(a) Write down the Lorentz transformation from Alice's coordinate sys-
tem to Bob's. (You may work in units where c =
: 1.)
(b) Alice observes a photon moving in the positive x direction with energy
E. What energy does Bob observe the photon as having?
(c) Eve is moving at speed u in the postiive x direction relative to Bob. Su-
pressing irrelevant y and z directions, find the Lorentz transformation
from Alice's coordinate system to Eve's. (Multiply two 2 × 2 matrices.)
(d) From your answer to the previous part, deduce the (one-dimensional)
velocity addition law in special relativity (the formula for Eve's speed
relative to Alice's).
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Step 1: Required to write Lorentz transformation equations
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