Let me preface this by saying I know very little about relativity. Last night a friend and I were discussing a particular scenario that will probably arise when humans begin to be capable of interstellar travel. Say you take off from earth and accelerate to some velocity and then coast until you get to a region of completely empty space with no visual references. Suddenly you decide that you want to bring your ship to a complete stop. To do so you would probably have to fire some reverse thrusters and accelerate opposite the direction you originally got going in. This is where we couldn't figure it out. How would you know when you had come to a complete stop? If you over fire the thrusters you could end up moving backwards rather than stopping. This led us to the idea that since mass is proportional to velocity under relativity, if you had a very good scale you might be able to determine the lowest possible mass that an object can achieve by trying out a few different directions of deceleration. Thus, to stop the ship you could decelerate until the object has that lowest possible mass. Does this make sense? I am confused about whether the people on the ship would see the mass of the object change with their velocity, and/or if that is what someone "outside the ship" would see. Also, is velocity only relative to something else, or is it somehow "non-relative" in that the speed of light is a constant value that can never be exceeded even in a completely empty universe? If it's the latter, it seems like you could figure out how to slow down to a complete stop in interstellar space somehow using the relationship between mass and velocity. Any thoughts?