Relativistic Doppler effect

The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity.

The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry.

In Diagram 2, the blue point represents the observer, and the arrow represents the observer's velocity vector relative to its surroundings. When the observer is stationary, the x,y-grid appears yellow and the y-axis appears as a black vertical line. Increasing the observer's velocity to the right shifts the colors and the aberration of light distorts the grid. When the observer looks forward (right on the grid), points appear green, blue, and violet (blueshift) and grid lines appear farther apart. If the observer looks backward (left on the grid), then points appear red (redshift) and lines appear closer together. The grid has not changed, but its appearance for the observer has.

Diagram 3 illustrates that the grid distortion is a relativistic optical effect, separate from the underlying Lorentz contraction which is the same for an object moving toward an observer or away.

Understanding relativistic Doppler effect requires understanding the Doppler effect, time dilation, and the aberration of light. As a simple analogy of the Doppler effect, consider two people playing catch. Imagine that a stationary pitcher tosses one ball each second (1 Hz) at one meter per second to a catcher who is standing still. The stationary catcher will receive one ball per second (1 Hz). Then the catcher walks away from the pitcher at 0.5 meters per second and catches a ball every 2 seconds (0.5 Hz). Finally, the catcher walks towards the pitcher at 0.5 meters per second and catches three balls every two seconds (1.5 Hz). The same would be true if the pitcher moved toward or away from the catcher. By analogy, the relativistic Doppler effect shifts the frequency of light as the emitter or observer moves toward or away from the other.

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