From the Starts With a Bang blog: Big Bang Alternatives: Could my light just get tired?
No, assuming photons lose energy as they travel along doesn't cut it.
You can plainly see that if you start with a blackbody spectrum, and cool it down without expanding it, you end up with the wrong spectrum for your observed radiation!
So that's the simplest explanation of why tired-light doesn't work. Remember this when you look for alternatives to a scientific theory: it isn't enough to make a better explanation of some of the observations; you have to account for them all.
Thing is, scientists have models sophisticated enough that they can calculate what we'd expect to see, given various changes. If someone wants to propose an alternative to the accepted theories, it needs to account for all kinds of things, not just one or two.
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