The General Relativity Elevator Thing

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O.k., correct me if I'm wrong because I'm new to the concepts of relativity and other stuff, but I have a question. General Relativity says that, in the vacuum of space, there is no way to tell whether a downward force is being caused by gravity or constant acelleration, right? Well, I thought of a way to find out. As your speed increased and aproached the speed of light, the rate of acelleration would slow down, right. I did some math out and found that, if you didn't know if you were on Earth or in one of these elevators, you could just wait like 130 minutes, then you would know. I don't know if this thought was good for anything, but I figured I'd share it anyway.
 
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Consider a rocket propelled by an engine that can deliver a constant thrust for a long time. Even though its coordinate acceleration as measured by an external observer must decrease as the speed approaches c, passengers inside the rocket would still "feel" a constant acceleration.
 
K, thanks. I guess I was confusing perspectives.
 
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