The photon wavelength of a receding star (moving away from the observer/receiver) has lengthened wavelength (redshift) at the observer/receiver. Light is emitted at light speed and - in this case red - wavelength, but the observer at the point of the photon arrival / detection can measure redshift. The speed also has to (seemingly but nonsensically) increase between the two points in order to make up for the speed of the source and arrive at light speed. How can photon wavelength and speed change between emission and arrival?
How can the Doppler effect apply when the speed of the arriving photon is the same as its emission speed?
I hope this is a better phrased question than the last one which was a bit of a ramble.
Your confusion is understable, and is based on the clash of the classical theory of light being electromagnetic waves (Maxwell) and the quantum theory of light (Planck) as composed of "quantum of action", later called photons.
As Planck is the father of quantum physics, his explanation has to prevail in the explanation of the dual behavior of light: "Light travels as electromagnetic waves, but are emitted and absorpted by matter as quantum of action (photons)".
There has not been a better explanation in 119 years, since Planck's Law. There is not a theory that can unify classical and quantum theories, so scientists have to deal with this dual explanation (which has no solution at sight).
This is the best I can do for you now. You have to accomodate your doubts around the basic fact of the dual behavior of light using our mathematics.
Edited by rhertz, 25 May 2019 - 10:06 PM.