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So, if you've ever read a sci-fi book you've seen it before probably: a ship like "babylon 5" (or the ship in "2001 A space odyssey" ) which rotates and creates artificial "gravity" by using centrifugal force... what i've never seen is anyone explaining what would actually happen to a ship that traveled while rotating like that in vacuum. I've heard some opinions that yes, if a ship had the engine to reach speeds such as let's say (just picking anything) 2/3 of $c$, then, as long as it is not traveling in the same direction as the rotation it would not affect the ship traveling at all. Is that right though? Does the theory of special relativity at large not affect centrifugal force in action at all?

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    $\begingroup$ You can't affect something that doesn't exist. I'm kinda kidding, there is a related article here en.wikipedia.org/wiki/Ehrenfest_paradox and this article is also helpful en.wikipedia.org/wiki/Centrifugal_force $\endgroup$ – user154420 Jul 2 '17 at 16:31
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    $\begingroup$ I don't think the OP considered rotation at relativistic speed, as that would kill everybody inside!!! $\endgroup$ – user154997 Jul 2 '17 at 18:27
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The paradox comes because a rotating disk should be contracted along the tangential direction of motion but the radius is not. The problem is that moving objects do not become visually Lorentz contracted, they are Terrell rotated. The following video illustrates this.

We consider a cube that is moving at a velocity $v$ that is passing in front of an observer. I have a diagram here. The first thing to note is that the back can emit a photon that reaches the observer. The cube move out of the way of these photons so the back is observable. This has the effect of making the cube appear rotated. In addition the front and leading edges of the cube emit photons on a path that is longer. This means photons leaving the front of the cube travel a distance $\sqrt{(d/2 + vt)^2 + x^2}$ distance, those leaving the trailing end $\sqrt{(d/2 - vt)^2 + x^2}$ while a photon that travels from the mid section only travels a distance $x$. Here $t$ is an increment in time for the cube to move from this initial position. This means the leading edge will appear rotated away and the apparent length contraction overall is then the appearance of a rotation. enter image description here

This means that for a rotating object this rotation makes the appearance of any side of the rotating body much shorter. In this video the rotation of the Earth is considered if it were rotating at a relativistic velocity. The rotation effect then means the observed side presented is a small section of any section of the rotating object. However, there is no contraction of the perimeter that then requires a contraction of the radius.

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  • $\begingroup$ If the cube has length $L$ and is moving with velocity $(v,0,0)$ being recorded on photographic plate parallel to one of the sides and the direction of motion. Than the time it takes for light from the back side to reach the photographic plate is $\frac{L}{c}$ and in that time the cube has moved $d=v\frac{L}{c}$. So the light that reaches the photographic plate was emitted at position $-d$. On the other hand the front side parallel to the velocity gets shrinked by $l\sqrt{1-\frac{v^2}{c^2}}$ . How exactly is this interpreted as rotation? $\endgroup$ – Alexander Cska Aug 19 '19 at 19:48
  • $\begingroup$ But is there a problem with such on the frame of this moving cube? What you illustrate is really how there is no general simultaneity of event in spacetime. $\endgroup$ – Lawrence B. Crowell Aug 21 '19 at 1:24
  • $\begingroup$ I don't understand how from this picture one can deduce rotation. $\endgroup$ – Alexander Cska Aug 21 '19 at 7:40
  • $\begingroup$ The main point is that Lorentz contraction in effect cancels out an optical effect in nonrelativistic physics that would elongate things. So Lorentz contraction exists and it is seen in that objects do not contract, though they may optically appear rotated or bent. $\endgroup$ – Lawrence B. Crowell Aug 22 '19 at 14:00
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So let's say the ship is put to spinning motion at the start of the journey.

Then when the ship accelerates, its spinning rate slows down according to observers at the launch platform. Spinning becomes time dilated. According to the observers on board the spinning rate stays constant. The ship can reach any speed below c. And the ship can move to any direction at speed below c.

The above is true only when the spinning and accelerating rocket emits reaction mass that is also spinning so that the angular momentum of the rocket fuel is the same before and after it has been burned. I mean when the rocket exerts no torque on the fuel and the fuel exerts no torque on the rocket, then the the spinning rate of the rocket obeys the time dilation formula.

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