Lorentz Transformations

Relativistic Doppler Effect

If you are driving towards a red traffic light ( = 650 nm) at a speed of approximately v = 0.17 c, then the light from the traffic light will actually appear to be green (' = 550 nm)! (0.17 c is approximately 5.010⁷ m/s.)

The Doppler effect: Motion towards or away from a source will cause a change in the observed frequency (or wavelength) as compared to the emitted frequency. All wave phenomena (e.g., water, sound, and light) behave in this way.

We will discuss below the Doppler effect and the concepts related to it as well as some formulas when relativistic effects are considered.

Suppose a source (for example a lamp or even better, a laser) emits light of frequency (or wavelength , remember that = c). Then, an observer moving with a speed v away from the source, will observe the frequency

This formula is usually called the relativistic Doppler formula. Note that ' < for all 0 < v < c, i.e., the frequency which the observer sees, is smaller than the "original" frequency in the inertial frame of the source. Thus, the observer moving away from the source will see a redshift in the frequency of the light, since light with lower frequencies are "more red" and light with higher frequencies are "more blue." On the other hand, an observer moving towards the source will see a corresponding blueshift. Note that it is only the relative speed that matters; an observer at rest in an inertial frame looking at a source moving away from him/her, would also observe a redshift.