Relativistic Doppler Effect

Claimed - Dev Sharma (Fall 2024)
The Relativistic Doppler Effect describes the wavelength and frequency of light due to relative motion between the source and an observer.

The Main Idea

The classical Doppler Effect describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. A common example is the change in pitch of the sound of a passing vehicle -- the noise has a higher pitch when the vehicle is approaching and a lower pitch when it is receding. This occurs due to the compression/stretching of the sound wave relative to the observer as it move through its medium (READ MORE HERE).

In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.

While we experience the classical Doppler Effect as a change in a sound's pitch, the Relativistic Doppler Effect causes a change in the frequency and wavelength of the light wave. If the light source is moving towards the observer, the light's frequency will increase and wavelength will decrease, causing it to "blueshift". If the light source is moving away from the observer, the light's frequency will decrease and wavelength will increase, causing it to "redshift".

It is important to note that there are other cosmological effects that can cause redshifting and blueshifting of light.

• Gravitational redshift occurs due to the influence of strong gravitational fields on light (READ MORE HERE).
• Cosmological redshift is caused by the expansion of the universe "stretching" light over large distances (READ MORE HERE).

These effects operate through different principles, and so are not covered in any greater detail in this article.

Derivation of General Relativistic Doppler Formula

Consider a given light source moving at relativistic speed [math]\displaystyle{ v }[/math], and an observer is observing the light at angle [math]\displaystyle{ \theta }[/math] relative to the source's motion.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

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