The equivalence principle as I understand it goes something like this:
Let's suppose you're in a black box in the middle of nowhere in space, and we accelerate this black box in some direction. You'd feel a force just like you would if you were in a gravitational field which was causing the same acceleration.
In fact there is no experiment that you can do to say for sure if you are in a gravitational field or just accelerating in some direction in a black box.
OK, so now let's imagine this elevator is being accelerated. Surely it can't accelerate at a constant rate forever, right? It's limited by the speed of light. So at some point or another the elevator will start to slow down. This sort of deceleration just does not happen in a gravitational field.
Where did I go wrong?
Best Answer
The point of the thought experiment isn't to say that the elevator can accelerate forever. The point is that acceleration is indistinguishable from being in a gravitational field. The acceleration doesn't have to exist for all time. However, just to address another issue...
This is incorrect. The speed of light limit doesn't say you will start to slow down once you get closer to the speed of light. The issue is that you are thinking in terms of absolute velocity, not relative velocity. The elevator cannot accelerate to move faster than the speed of light relative to something else. This doesn't affect the acceleration you would feel in the elevator though. If we had some magical infinite fuel source, then indeed you would feel the same acceleration in the elevator forever. The speed limit applies to an outside observer who would see your speed relative to them approach but not reach the speed of light.