Redshift and blueshift in relativistic doppler effect

[qazadex]

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):
[itex]\frac{\sqrt{1 - v^2/c^2}}{1+\frac{v}{c}\cos{\theta}}[/itex]

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.

 

[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.

 

[jartsa]

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.

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.

 

[qazadex]

Thanks for the answers: it makes pretty much perfect sense now.

 

[sardar]

The redshift and blueshift phenomena in the relativistic Doppler effect can be understood by considering the effects of time dilation and the relative motion between the source of light and the observer.

When an object emits light, it creates a series of wavefronts that propagate through space at the speed of light. However, if the object is moving relative to the observer, the observer will perceive these wavefronts as arriving at a different frequency due to the effects of time dilation.

In the case of redshift, the object emitting light is moving away from the observer, causing the wavefronts to arrive at a slower rate. This means that the frequency of the light perceived by the observer will be lower, resulting in a longer wavelength and a shift towards the red end of the spectrum.

On the other hand, in the case of blueshift, the object emitting light is moving towards the observer, causing the wavefronts to arrive at a faster rate. This means that the frequency of the light perceived by the observer will be higher, resulting in a shorter wavelength and a shift towards the blue end of the spectrum.

The choice of frames of reference is important in understanding the relativistic Doppler effect because it allows us to consider the effects of time dilation and the relative motion between the source and observer. By looking at the situation from different frames of reference, we can gain a better understanding of the observed frequency shifts and how they are affected by the motion of the objects involved.

Overall, the redshift and blueshift phenomena in the relativistic Doppler effect can be intuitively explained by considering the effects of time dilation and the relative motion between the source and observer. These concepts are fundamental in understanding the behavior of light in different frames of reference and their implications for the observed frequency shifts.