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If the universe wasn't expanding, would light still be redshifted after traveling some distance?

Is there a way of being sure that it's the expansion that causes light to redshift and not just a natural phenomenon for light to redshift as it travels, regardless of whether space is expanding. In the latter case, the only way expansion of space could affect the redshift would be by making light travel a longer distance.

Edit: So I've come across the term 'Tired light' in an SE answer but it doesn't really explain why there aren't supporters for this theory. So, why aren't there?

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