Show that the wave equation: ?²? = (1/c²)(?²?/?t²) is invariant under the Lorentz transformation: The Lorentz transformation is: (the symbols have their usual meaning) x' = ?(x - vt) y' = y z' = z t' = ?(t - vx/c²) ? = (1 - v²/c²)^-1/2
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Now, let's consider the Lorentz transformation: X' = γ(X - vt) t' = γ(t - vX/c²) where X' and t' are the coordinates in the moving frame, X and t are the coordinates in the stationary frame, v is the velocity of the moving frame relative to the stationary Show more…
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