Understanding Redshift: The Role of Relative Motion between Emitter and Absorber

[Harry17]

As light interacts as a particle and when being absorbed or emitted by an electron that is done instantaneously, that is, no time between the photons energy not being contained (I’m unsure as to whether or not this is the correct word) within the electron to being contained within it, how does redshift occur since it’s due to relative motion between an emitter and an absorber, since the photon was emitted in a single instant where (presumably) no motion can occur?

There’s likely a very simple answer due to a flaw in my reasoning, I’m as yet unable to find it though

 

[PeterDonis]

As light interacts as a particle and when being absorbed or emitted by an electron that is done instantaneously

Why do you think this must be the case? We don't measure "how long" it takes for light to be absorbed or emitted by an electron; it's not even clear that it's meaningful to ask how long it takes.

But even if we assume for the sake of argument that your statement here is correct, it still doesn't support your argument. See below.

how does redshift occur since it’s due to relative motion between an emitter and an absorber, since the photon was emitted in a single instant where (presumably) no motion can occur?

Redshift is due to relative motion between the emitter and the absorber. Your claim is that light is emitted instantaneously and absorbed instantaneously, so therefore there is no relative motion between the photon and the emitter when it is emitted, and no relative motion between the photon and the absorber when it is absorbed. But that in no way means that there is not relative motion between the emitter and the absorber.

 

[PeterDonis]

Your claim is that light is emitted instantaneously and absorbed instantaneously, so therefore there is no relative motion between the photon and the emitter when it is emitted, and no relative motion between the photon and the absorber when it is absorbed.

Note that even if we assume that light is emitted and absorbed instantaneously, that still does not require that there is no relative motion between the light and the emitter or absorber. Light is massless, so it does not require time to accelerate; it can (at least in the approximation we are using here) instantaneously start or stop moving at the speed of light, so it can instantaneously have motion relative to the emitter as it's emitted, and instantaneously have motion relative to the absorber as it's absorbed.

But the more important point is the one I made in my last post, that the relative motion that is pertinent for redshift is the relative motion between emitter and absorber, not relative motion between the light and either of those.