Question

In the context of the Doppler effect, how does the change in observed frequency for a light source moving away from an observer relate to the relativistic shift in the wavelength of the emitted photons?

Accepted Answer

When a light source moves away from an observer, the light undergoes a redshift, meaning the observed frequency decreases and the wavelength increases. This happens because the light waves are stretched out as the source travels in the opposite direction of the emitted light. In relativistic terms, this phenomenon includes two distinct effects: the classical Doppler effect, caused by the change in distance between the source and observer, and time dilation, which is the physical process where time passes more slowly for an object moving at high speeds relative to an observer. Imagine a clock on a fast-moving spaceship appearing to tick slower to a stationary observer; similarly, the internal oscillations of the light source appear slowed down, further lowering the frequency. The relationship is mathematically defined by the relativistic Doppler formula, which combines these effects to show that the observed wavelength becomes significantly longer than it would be in classical physics. Because the speed of light is constant for all observers, the light cannot simply &#x27;travel slower&#x27; to compensate for the distance, so the energy of the photons must decrease, manifesting as this shift toward the longer-wavelength, red end of the light spectrum.

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In the context of the Doppler effect, how does the change in observed frequency for a light source moving away from an observer relate to the relativistic shift in the wavelength of the emitted photons?