Theoretically if in early years the earth was moving at an astronomically different pace (whether in orbit or rotation, whatever sounds better) wouldn't that alter the science of carbon dating? As I understand time relativity, If the speed at which the earth was moving changes, the elements and organisms there-in would experience time at a different rate. Would we not expect that carbon would decay faster? I know it's just theory but I'd like to know if this theory could be proven false. And is there any existing research that you are aware of that would support or debunk this theory?
The laws of physics are valid and the same in all reference frames. This is the principle of Special Relativity. It would make no difference to us if the Earth was travelling at a different speed. We, as a part of the Earth, would make the exact same measurements as we do now. (The only difference would be how everything appears to an external observer, we would appear slower to one.)