Doppler effect of light spectrum

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When we first realized that the further away a galaxy is the further towards the red side of the spectrum it was, we beleived this to be do to the expansion of the universe? Wouldn't it have been simplier to say that the further away a galaxy was the further the wave function stretched over space time? Just like in a pond? I know this is crazy as it would spell the end of current consmology. I just want to know why the second one didnt make more sense?
 
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As far as I understand the wave function doesn't stretch, it stays consistent in it's wavelength. It is the expansion of the universe that is causing it to outstretch as the spatial distance itself in between wavelength peaks/troughs is actually growing.

EDIT: Oh you are asking wouldn't it be simpler to conclude that a property of waves is that over long distances they slowly stretch? It probably contradicted already known properties of waves but I'm not certain.
 
yes, I figured it had to do with the fact that it has been proving that light does not stretch. I was wondering what this proof is?