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this post was submitted on 12 Mar 2024
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Relativity says yes. There's no absolute speed, only relative speed; within the local reference frame of the ship, everything will continue to work normally, including the force experienced due to acceleration.
The ship is not actually going to reach the speed of light (as seen by an outside observer) though. The faster the ship goes, the more its (observed) mass increases, and the 9.8m/s² acceleration will have less and less of an effect. But to the people inside the ship, it appears as though they can accelerate indefinitely, going faster and faster at their steady rate of acceleration. Due to relativistic effects, it'll never look like they are passing any objects outside the ship at more than the speed of light; instead it will appear as though the distance they have to travel is compressed, so they don't have to travel as far.
You can think about it this way. In relativity:
A minor nit pick. It's worth noting that increasing mass is an inaccurate view. It works in the simple examples, but can cause confusion down the line.
Instead, an additional term is introduced. This term, while it could be combined with the mass, is actually a vector, not a scalar. It has both value and direction, not just value. This turns your relativistic mass into a vector. Your mass changes, depending on the direction of the force acting on it! Keeping it as a separate vector can improve both calculations and comprehension, since comparable terms appear elsewhere (namely with time dilation and length contraction).