I was reading the thread entitled "photon frequency" and I now have the following question:

 

Is photon frequency a frame dependent quantity, and if so what is the formula which discusses how f transforms?

 

I expect to see a discussion of the Doppler effect, but I really don't know what kind of answers I will get.

 

Suppose that the frequency of something is f₀ in it's rest frame. What is its frequency in a frame in which it is moving with speed v?

 

For example, let there be a pendulum swinging inside of a spaceship. Let the time it takes for the pendulum to go back and forth once, be amount of time T, which we can call the period of this pendulum. So this amount of time T, makes sense in the ship frame, which is a reference frame in which the center of inertia of the ship is at rest. In this frame we will define the rest frequency of the pendulum mathematically as follows:

 

f₀ = 1/T

 

So the question is, what is the frequency of the pendulum in a reference frame in which the ships speed is v. How does frequency transform?

 

Thanks

In special relativity, if the frequency in a moving spacehip is f, the frequency measured on Earth is given by: f'=\gamma f(1+v cosA/c), where v is the ships speed,

c the speed of light, \gamma=1/sqrt(1-v^2/c^2), and A is the angle between the photon direction and the observation point on earth, as measure in the space ship.

This equation is different than the acoustic Doppler effect, but is usually called the

"Relativistic Doppler shift".