The group velocity of any wave transforms under Lorentz boosts as a particle velocity, and so by the Einstein velocity addition relations. This is expected for the velocity of energy transport in spite of the presence of a medium and so a preferred frame. The phase velocity has the same transformation property only when the group and phase velocities are parallel and the product of their magnitudes is equal to c2. A proof is given of the relativistic group velocity transformation which is simple and novel, and which uses spatial filtering concepts to derive the formula for group aberration as a consequence of that for phase aberration. This gives some physical insight into the previous proofs based on a four‐vector analysis.
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© 1992 American Association of Physics Teachers.
1992
American Association of Physics Teachers
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