(a) Consider a wave with dispersion relation (k). Show that the group velocity u = k...
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(a) Consider a wave with dispersion relation ω(k). Show that the group velocity u = ∇kω transforms under a Lorentz transformation exactly like a particle velocity.
(b) Show that the phase velocity up = (ω/k)k̂ transforms under a Lorentz transformation exactly like a particle velocity when ω = c|k|.
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To show that the group velocity u k behaves like a particle velocity under a Lorentz transformation we need to demonstrate that it transforms in a similar way to how a 4velocity of a particle does Let...View the full answer
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