Suppose you are in a rocket with no windows, traveling in deep space far from other objects. Without looking outside the rocket or making any contact with the outside world, explain how you could determine whether the rocket is (a) moving forward at a constant $80$% of the speed of light and (b) accelerating in the forward direction.
This is one of the discussion questions from the book ‘University Physics with Modern Physics’ (Q $38$, Page $124$, Ch $4$: Newton’s Laws of motion.
This is a discussion question anyway, not a numerical problem so I hope it does not get discarded here)
(b) If the rocket is accelerating forward, I can do a few things to sense the acceleration. For example, if I put a tennis ball on the floor, it should roll backwards without any apparent force acting on it. Similarly, If I am sitting in a chair, I should be pressed backwards, and I should be able to feel the acceleration, and hence the contact force acting on me. Likewise, I can’t play catch with a tennis ball with my friend. He will perceive the ball coming at him faster, and I would perceive it moving slower (assuming he is standing to my right, in the direction of rocket’s acceleration). From these observations, I should be able to say that the rocket is accelerating, in the direction opposite to the direction in which the tennis ball on the floor starts to roll.
(a) But what if the rocket is moving at a constant velocity at $0.8c$? Since there are no windows, is it possible to tell if the rocket is at rest or moving at $0.8$C?
I googled it, and some of the answers explained that since “Constant velocity means no acceleration, and therefore you are in freefall. You have mass, but not weight, so a bathroom scale would read $0$.”
I understand that during freefall, a bathroom scale would always read $0$. But doesn’t freefall mean gravity is the only force acting on us? Since the question says that the rocket is in deep space far from other objects, how can I be in freefall? The question explicitly says “the rocket is moving forward at $0.8c$, which means it is moving straight and not orbiting any planet or a star. How am I in free fall then?
If I’m not in free fall, is it possible to determine whether the rocket is moving forward at $0.8c$, as the question asks?