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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?

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    $\begingroup$ This was first answered by Galileo. en.wikipedia.org/wiki/Galileo%27s_ship $\endgroup$
    – mmesser314
    Commented Dec 7, 2019 at 6:41
  • $\begingroup$ "the rocket is in deep space far from other objects, how can I be in freefall" Remember that gravity has infinite range. And "forward" movement is not the same as "straight". $\endgroup$
    – hdhondt
    Commented Dec 7, 2019 at 9:07
  • $\begingroup$ Free space (with no gravitational field) is also an inertial frame of reference, not just free fall. $\endgroup$
    – bemjanim
    Commented Dec 7, 2019 at 11:14
  • $\begingroup$ Are we assuming special relativity or Newtonian mechanics? If special relativity holds true then it is impossible to determine an absolute velocity. $\endgroup$
    – bemjanim
    Commented Dec 7, 2019 at 11:18
  • $\begingroup$ @hdhondt Gravity does have infinite range. But why would the question explicitly say that the rocket is in deep space "far from other objects"? Isn't that implying that the rocket is not in a orbit around another object? Also, can it stay in an orbit around another body when moving at that speed, $0.8$C? Also the question says that its speed is constant. As far as I know, neither earth, nor moon, or any other celestial body orbits another body at constant speed. Their orbit is elliptical? $\endgroup$
    – 4d_
    Commented Dec 7, 2019 at 12:24

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The question you quote appears to suggest that you are so far from other objects that their gravitational effects can be overlooked. If that is the case then the answers are:

a. You cannot determine whether the ship has any specific speed relative to anything else. Indeed, the implicit assumption that the ship can have an absolute speed of 0.8c without any specified frame of reference is a faulty one.

b. If the ship were accelerating in the forward direction then anything not fixed within it would drift to the back.

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  • $\begingroup$ "Indeed, the implicit assumption that the ship can have an absolute speed of 0.8c without any specified frame of reference is a faulty one." Is it possible to determine from an internal reference frame (any inertial reference frame) that the sheep is moving at $0.8c$ ? $\endgroup$
    – 4d_
    Commented Apr 16, 2022 at 3:50

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