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Before I get into the actual question, I'd like to say that my only knowledge on Einstein's Theory of Relativity (both Special and General) have been obtained through about an hours worth of videos and a book about him, Einstein: His Life and Universe So please correct me if I'm wrong about the definitions, origins, etc.

So, in one of Einsteins thought experiments, he imagines two people in separate boxes, one in a gravitational field while the other is moving upwards at a constant velocity (I'm sure you probably already know this thought experiment). Anyways, Einstein states that with no reference to anything outside the box and the only information obtainable is what is happening inside the box, makes the conclusion that its pretty much impossible to figure out which one they are part of, the gravitational field, or moving upwards.

Instead of a box that moves upwards, what if it was something like a long hallway; say you shot a gun at one end to the other. Would the bullet move relative to the velocity of the box/hallway (a straight line), or would it appear to fall downwards as the box moves upwards?

PS: This is my first time using this website so sorry if it seems a bit unprofessional :P

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  • $\begingroup$ As pointed out by Dwagg: you misstated the thought experiment. You managed to get velocity and acceleration confused, that's really weird. I mean, those words aren't specific to physics, those words are used in everyday life. (Example: the specifications of a high performance car.) $\endgroup$
    – Cleonis
    Commented Mar 15, 2019 at 22:17

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I think you misstated the thought experiment. There is a proposed equivalence of an observer in an elevator at rest in a gravitational field and an observer in an elevator moving upwards at a constant nonzero acceleration.

To answer your hallway question: if the box is always moving at constant velocity then the bullet will not fall relative to the box. If the box is moving at constant nonzero acceleration then the bullet will appear to fall.

Indeed, this is evidence for the aforementioned equivalence. You already know that a bullet fired on earth (at rest in a gravitational field) will fall, which is why long range shooters should aim slightly above their targets.

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  • $\begingroup$ I was just thinking that if it did fall, it would happen fairly quickly as to replicate gravity on earth, the box would have to go upwards several meters per second, making the bullet hit the ground almost instantly. Also, could you define nonzero acceleration, as I think I've misinterpreted the definitions of both acceleration and velocity. $\endgroup$
    – JEREMIAH ANDREWS
    Commented Mar 15, 2019 at 22:28
  • $\begingroup$ Acceleration is change in velocity per unit time. It is measured in $m/s^2$ (meters per second per second), and velocity is measured in $m/s$ (meters per second). You may know that the gravitational field of earth has strength $g= 9.8 m/s^2$-- it is measured in acceleration units. $\endgroup$
    – Dwagg
    Commented Mar 16, 2019 at 12:38
  • $\begingroup$ The bullet won't necessarily hit the ground almost instantly. Another thought experiment may help to clear confusion. You're in a plane traveling through the sky at some $300 m/s$. You toss an apple in the air directly above yourself. Does it fly to the back of the plane? Why not? $\endgroup$
    – Dwagg
    Commented Mar 16, 2019 at 12:40

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