Suppose there's a spaceship accelerating at a constant rate, say g, thanks to some magic rocket engine. This engine creates a constant force on the ship, which is sufficient to accelerate its constant mass at a constant rate. Supposing that the floor is perpendicular to the line of travel, the occupants will feel as though they are standing in Earth's surface. To those occupants, the simulated feeling of gravity will continue indefinitely, even though to an observer at rest relative to their launchpad will perceive their acceleration to decrease as they approach the speed of light, correct? That's my intuitive sense of the situation, but I don't really understand why it would be true. Can someone explain further?