The relativistic transformation law that relates the coordinates seen by an observer (2) moving at velocity v relative to an observer (1) is x₂ = (cosh ?)x₁ ?(sinh ?)ct₁, ct₂ = (cosh ?)ct₁ ? (sinh ?)x₁, where sinh ?/ cosh ? = v/c.The similarity to rotation in Euclidean space by an angle?. Confirm that under this transformation the space time distance (21.24)

between two events is the same for both observers. Check that in the limit v ? c the Newtonian transformation rules described in the previous problem are reproduced.

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A? = Ax? + Ay² + Az? – c²ar²