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• Two inertial frames S and S′ are in the standard configuration, with relative velocity v along the line of the x and x′ axes. Consider any two events, 1 and 2. (a) From the Lorentz transformation (1.37), derive expressions for the separations Δx′, Δy′, Δz′, Δt′ (where Δx′ = x′2 − x′1, etc.) in terms of Δx, Δy, Δz, Δt. (Notice how the transformation of Δx, Δy, Δz, Δt is identical to that of x, y, z, t.) (b) If Δx = 0 and Δt = 4 s, whereas Δt′=5s, what is the relative speed v, and what is Δx′?
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