# Redshift and blueshift in relativistic doppler effect

1. May 25, 2014

I'm looking for an intuitive explanation for the redshift and blueshift phenonema that occurs when a light ray is emitted transversely.

According to wikipedia:

Assuming the objects are not accelerated, light emitted when the objects are closest together will be received some time later, at reception the amount of redshift will be 1/γ.

Light received when the objects are closest together was emitted some time earlier, at reception the amount of blueshift is γ.

Now these expressions can be derived using this formula(a generalized version of the doppler shift):
$\frac{\sqrt{1 - v^2/c^2}}{1+\frac{v}{c}\cos{\theta}}$

However, I'm trying to understand based on the principles of time dilation. The redshift situation makes sense: because of time dilation, successive wavefronts arrive by a factor of λ slower according to the receiver, so the f' is 1/λ * f. However, this logic fails with the blueshifting. A way in which the blueshifting expression could be derived is by looking at the situation from the source of the light, and seeing waves get absorbed by a factor f γ slower, which would lead to the above expression for blueshifting. However, I'm not sure why these frames of reference would need to be chosen.

Any help would be appreciated.

2. May 25, 2014

### dauto

I think you already answered your own question. These are indeed just the time dilation factors as seen from either the source or the receiver points of view. The point is that the trajectory of the ray is perpendicular to the relative velocities between the frames. In the red shift case the trajectory is perpendicular from the point of view of the receiver while in the other case it is perpendicular from the point of view of the source. When the trajectory is perpendicular, Doppler effect is given by time dilation alone.

3. May 25, 2014

### jartsa

I would say:

When the objects are closest together according to the receiver, then the amount of redshift will be 1/γ according to the receiver.

And that is because the reciever sees the distance staying constant at that point, so he observes the time dilation and nothing else.

4. May 25, 2014