It's true that light is affected by gravity. This was first seen in experiment in 1919. The main insight of Einstein's theory is that the speed of light in a vaccum, called c, appears the same to all observers irrespective of their situation.
To clarify, I'm not suggesting we automatically throw out any suggestion that c varies. I said throw out stuff like freeway's link back there because it's full of really bad science.
If we're going to suggest that c varies we should be clear what we mean by that. I couldn't find any serious opposition to Einstein's idea that c is constant
now, but there is a
minority opinion in physics which suggests that it has changed over time.
If you change c you have to change a lot of physics. The famous equation e=mc2 describes how much energy is given off by the sun and by radioactive decay. If c was bigger, this energy would be very much bigger. If c was much higher at a time when life existed this would raise the question
were Adam and Eve toast?
Relativity is a strong theory because it explains a lot of different things and matches very well with experimental data. I'm reading that no-one has yet produced a full theory using a variable speed of light which matches the data as well. It's possible that somebody might do this, and then physicists could evaluate the merits of the competing theories. The toast problem would suggest, though, that if c was much higher in the past it happened a very long time ago. The physicists who propose this are talking about a time just after the big bang, because they're working on the
horizon problem.
I must admit, though, that I don't fully understand what the speed of light has to do with the age of the earth. I'm guessing it's to do with the speed of radioactive decay and the effect that would have on the radiometric dating that produces the 4.5 billion years figure, but I'd be grateful if the YE people could clarify that for me.