Aberration of particles and wave fronts

This is the representation of a 2+1-dimensional space time, x and y is the ordinary plane (in dark green), ct the time is counted in the vertical. A wave front is moving in the y-direction with the speed of light. Its trace through space-time is the yellow plane. The world-line of an embedded photon is drawn in dark yellow. It lies in the y-ct-plane. The world-lines of two observers in relative motion are added.

The observed directions of the photon are found by projecting its world-line onto the plane of simultaneous events (dark green). The two observers see different directions.

The observed direction of the wave front is found by intersection of its trace (the yellow plane) with the plane of simultaneous events. When we stick to absolute simultaneity, no aberration is found. Aberration of wave fronts requires relative simultaneity. The plane of simultaneous events for the observer moving to the left must be the light green one.

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