Doppler effect and speed of light as a constant.

[paalfis]

The question "If light speed is constant, how do you explain the Doppler Effect?" has been asked a lot in the internet. Anyway, I haven't found one concise answer. In the book Kleppner&Kolenkow Mechanics there is a brief explanation of the Relativistic Doppler Effect, but as usual in this topic, it uses the property of light speed being constant to explain it (it doesn't deduce this last property).
So, the right questions to ask, in my opinion are these:

• How would you (cleverly) use the red shift property to deduce that light speed is constant?
• In terms of the properties of light as a wave, what happens to the wave in order to change it's wavelength to red but maintain it's speed.

 

[Simon Bridge]

1. You can't. The phenomenon does not depend on lightspeed being invariant (note: not "constant").
"invariant" means that all inertial observers measure the same value.
However, you can compare different models experimentally and show the most useful consistency comes from the invariant lightspeed case.

2. $c=f\lambda$ so what do you think happens to allow the speed to be the same when the wavelength is different?

In considering special relativity, you have to be very careful with your language or you'll get confused.
Forinstance, it is natural to think that a light source gets bluer if you move towards it - but this language is nonsence in SR.
The "you" in the sentence is the observer.
In SR, all observers are stationary.
So how can "you" be "move towards" the light source?

Instead you have to compare two situations.
i.e. two otherwise identical light sources, one stationary wrt you and the other moving towards you, will show a difference in their frequencies: the moving one is bluer. The blueness is a manifestation of the momentum it carries. The speed of the light from each source can be measured and will be found to be the same.

And that is the succinct description for how the doppler shift happens when the speed of light is invarient.

You should realize that the invariance of the speed of light is not a deduced property, but a postulated one. It is needed in order to make a definition of what we mean by "simultaneous events".