system
Given the following post, respond as if you're commenting on Reddit:
human
Could a gradual (but accelerating) slowdown of the 
speed of light account for the appearance of an 
increasingly expanding universe?

First, please understand that I am NOT referring to the c-decay theory that young-earth creationists try to use to reconcile astronomical evidence with the notion of earth being only maybe 10 millennia old.  I am instead asking how we could (and presumably do) know that the acceleration of the expansion of the universe is due to the actual expansion of the universe and not the the fact that our meterstick (the light-year) got shorter over time?

Consider a universe with only two bodies; a star and an observing planet a great distance away, stationary to one another.  Then assume that the speed of light decays over time, and the rate of decay increases over time; not the lifetime of the light in question, but all light in this particular universe.  Would not the light from the star appear redshifted to the planet?  Each photon that came out would be slightly faster than the next to come out, which would be slightly faster than the one that follows it, and so on and so on.  As the decay of the speed of light grew, the apparent redshift would also increase, without any necessary movement on the part of either body.

But even if that was the case, how would we KNOW?  Assume the planet has a ship that can travel at relativistic speeds, say .9c; as the speed of light decreases, .9c also decreases, and so the trip would take longer each time, which, for all intents and purposes I can think of would seem to be identical to an increase in the distance between the two bodies.

I'm just a dabbler in phsyics and astronomy, but I can't see how this result would fail to stand if extended to our universe; the rate of c-decay would be very slow (probably requiring at least geological timescales to be noticible), but it would still make sense.  It also seems to me more plausible for c to decay (a form of entropy) than objects accelerating away from us with no visible input of energy (anti-entropic behavior)(although I realize both notions are based off probably-inapplicable analogy rather than a proper understanding of the relevant physics).

I'm sure that someone has proposed it and there's good reasons for dismissing it, but I can't think of any way we could tell the difference between acceleration and c-decay.  Help!
gpt
No.

You mention doppler shift based purely on time of arrival of photons. An analogy to your example: If we had a pulsar and its pulses were growing further apart then we could say either it's rotation is slowing or it is accelerating away or more unrealistically the speed of light is slowing down. However, if we have a spectral line for which we expect to be a certain colour then it doesn't matter how spread out the photons are they are ALL the wrong colour.