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Lorentz Transformation
1. Inverse transformation
The Lorentz transformation from (x, y, z, t) to (ξ, η, ζ, τ) is
What is the inverse transformation from (ξ, η, ζ, τ) to (x, y, z, t)?
Find two ways of arriving at it.
Hint: one way is hard; one way is easy.
2. Transforming light
A point propagating at the speed of light moves according to
ξ = c τ η = ζ = 0
in the inertial frame of reference with coordinates (ξ, η, ζ, τ). How is this motion described in the inertial frame of reference with coordinates (x, y, z, t)?
Bonus entertainment
Redo the last calculation for the more general case of a point moving at the speed of light described by
ξ2 + η2 + ζ2 = c2.