Is this a valid implication/alternative explanation of universal red-shift? I thought I'd ask this when I read this question about light clocks.
I had speculated this way: If light speed determines the rate of time, could the speed of light be varying over time and we be unaware of it? We measure light speed by itself.
But if light speed was varying over a scale of minutes or hours, we'd see variation in the Sun's spectrum over time, either red shift or blue shift, and we don't.
If it was varying over a period of years, we'd see variation in the spectra of stars, and we don't.
If it was varying over a period of billions of years, we'd see variation in the spectrums of distant galaxies, and we do.
Is this a possible implication of universal red-shift? Or even an alternative to the expansion explanation?