Section 3.5: Understanding the Relativistic Doppler Effect

Add light λ = nm

speed of light source = * 106 m/s

Please wait for the animation to completely load.

In the animation, add a light source (in the visible part of the spectrum).  Change the speed of the light source and then choose whether the source is moving toward you or away from you and observe what happens. You can measure the wavelength of the light (given in nm) by clicking in the animation. Restart.

Just as you hear different pitches (frequencies) of sound when a car goes past (due to the Doppler effect), light from a moving source is Doppler shifted as well. The Doppler effect for sound waves depends not only on the relative motion between you and the source of sound, but also on the relative motion between the sound source and the air. Initially, scientists thought light had to propagate through some medium which they called the ether.  This ether provided an absolute reference frame for light. The speed of light would be measured relative to this reference frame, and if you were moving relative to the ether, then you would measure a different speed of light. Special relativity discards this: the speed of light is the same no matter the reference frame. There is no ether and no absolute reference frame. Therefore, the Doppler shift for light is simply due to the relative motion of the two reference frames (the source and receiver) and is given by

1/λ' = (1/λ)((1 −/+ v/c)/(1+/− v/c))1/2 ,                    (3.9)

for objects moving away from each other (upper signs) and for objects moving towards each other (lower signs). Here λ is the wavelength as measured in the frame of the moving light source, and λ' is the wavelength as seen in your reference frame.

The Doppler effect provides us with a great deal of information about our universe. For example, light from distant stars is  red-shifted, that is, the light from the stars is shifted to longer wavelengths (red side of the spectrum). The atoms that make up stars have a unique light spectrum (as we will see later when we explore the nature of atoms) and when we view spectra from stars, we find the wavelengths to be longer than expected. The wavelength shift means, according to the Doppler effect, the stars are moving away from us. In fact, everywhere we look in the universe, things are moving away from us. This does not mean we are the center of the universe, it simply means that the universe is expanding (think of points on the surface of an expanding balloon: as the balloon expands, all points move away from each other, but no one point is the center of the expansion).  By measuring the Doppler shift of the wavelength of light we receive from various light sources throughout the universe and knowledge of how far away those sources are, we can calculate how fast the universe is expanding and therefore an approximate age of the universe.

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