I will not pretend to be an expert. But I’m a little tired of seeing this argument because it’s so easily proven not to be a good argument for the old earth theory.
The argument goes something like this:
“If the speed of light never changes and nothing has interfered with our perception of that light, then the speed of light tells us how far away a light-emitting object is.”
In other words, if the speed of light is 671 million miles per hour, that translates to 16,104,000,000 (16.1 billion) miles per day or 5,865,882,000,000 (5.9 trillion) miles per year. So if a light-emitting object is 5.9 trillion miles away from us, it would take one year for that light to reach us. If a given star is 5 million times that far away from us, and if the speed of light doesn’t change, that means the light took 5 million years to get to us, which means the earth is at least 5 million years old.
The most important point to make regarding this whole concept is that we don’t know what the speed of light was 500 years ago or a thousand years ago or a million years ago. Maybe it was slower. Maybe it was faster. We simply cannot assume that the speed of light never changes.
This may have been something to laugh at before 2002, when a group of scientists casually commented in a paper about black holes that, hey, it looks like the speed of light is slowing down . In fact, it’s been slowing down for the approximately 300 years over which we’ve been measuring the speed of light .
Obviously, scientists everywhere hated this idea because it would demand a number of huge changes to scientific observation. For example, if the speed of light is slowing down, this would mean there was less radiation yesteryear than today, which means our radiocarbon dating measurements have always been incorrect—specifically, over-estimated . (Side note: this may explain why there are numerous conflicts between carbon dating and observations of the same fossils, e.g., the existence in fossils of DNA, blood cells, blood vessels, proteins, and other structures which should have decayed in far less than a million years .)
Nonetheless, what we have is a slowing speed of light. At our current vantage point, we have no idea whether it looks like A or B or even C and whether the timespan is over several billion years or several thousand years.
In short, the speed of light is not proof of a young earth, nor of creationism. However, it is also not proof of an old earth theory. Since we know it is changing but we can’t know what it was doing in the past, it cannot be used in the present as evidence of what happened in the past.
 Davies, P.C.W., Davis, T.M., & Lineweaver, C.H. (2002). Black holes constrain varying constants. Nature, 418(6898):602–603. doi: 10.1038/418602a. (full text not freely available online, but for now, try this link: http://sci-hub.cc/10.1038/418602a)