Let's see about that.Wrong. To talk about a Doppler *shift*, we need to compare what two different observers will measure. The shift is the difference of the frequencies.
Ok. Now you have managed to clarify your position to the point that the frequency difference comes from the changed relative speed of the observer's two reference frames. The emitters reference frame is unknown. So what you have for calculating the frequency change in the observe's frames is:Yes, actually. The observer can measure the frequency of the light. She does not know the frequency of the light from the emitter, so cannot know the Doppler shift between the emitter and her. However, she *can* find the shift between *her* two frames: one approaching and one receding.
The Doppler shift is a difference of frequency between two different frames. If nothing about the frame of the emitter is known (for example, the frequency of the light in the emitter's frame), then no shift between that frame and the observer can be known.
- in both frames the speed of the wavefronts relative to the observer is the same which is c
- in the first reference frame the observer has accelerated to velocity v1
- in the second reference frame the observer has accelerated to v2
Let's look at the calculations of your model again:
"Since the wavefront moves with velocity c and the observer escapes with velocity v, the time (as measured in the reference frame of the source) between crest arrivals at the observer is t = lambda /(c-v)"
According to your argument above the frequency difference comes from the velocity difference in the two reference frames of the observer (v1 and v2), so the subtraction should be v2-v1 or v1-v2. Why is there a velocity of the observer subtracted from the velocity of the wavefronts which is constant to the observer ALWAYS?
The equation violates the constant speed of light law.