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If motion is relative, (so if X was stationary and Y was moving at v m/s, we could think of this as Y being stationary and X moving at -v m/s), could we not create a scenario in which a stationary body is relatively moving faster than light?

Suppose that a rotating body is situated at an extremely large distance from a stationary object.

If someone was standing on the rotating body, would the stationary object not appear to be moving at speeds much faster than light?

$ω = v/r$

$r = \infty$

$v = \infty \omega$

$v = \infty$

(using $\infty$ to refer to an arbitrarily large number, not any actual infinity)

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    $\begingroup$ The "reference frame of [the] rotating body" is not an inertial reference frame, so the rules you learned for things that happen in inertial reference frames don't apply here. $\endgroup$
    – The Photon
    Commented Apr 23 at 0:30
  • $\begingroup$ @ThePhoton is there any reason why an observer on the rotating body has to be accelerating? Is it not an identical scenario to them being completely stationary, and the object rotating around them? $\endgroup$
    – bbqribs2000
    Commented Apr 23 at 0:36
  • $\begingroup$ Infinity is not a number you can do algebra with like that, so those manipulations don't make sense at any state of calculation. $\endgroup$
    – Triatticus
    Commented Apr 23 at 0:44
  • $\begingroup$ @Triatticus I'm just using infinity to represent an arbitrarily large number, should've been more clear. $\endgroup$
    – bbqribs2000
    Commented Apr 23 at 0:58
  • $\begingroup$ @bbqribs2000, If the observer is floating above the rotating body, not rotating, then it's possible that their rest frame is an inertial one. But also, the distant object won't be moving at greater than c in that frame. $\endgroup$
    – The Photon
    Commented Apr 23 at 2:54

2 Answers 2

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A rotating reference frame is not inertial. The fact that light travels at $c$ as well as the fact that massive objects travel at $v<c$ are both facts that only apply to inertial frames.

In non-inertial frames the condition is that light travels on null geodesics and that massive objects travel on timelike paths. In an inertial frame these general conditions reduce to the usual restrictions. But in other frames the more general restriction still holds.

In a rotating frame the velocities of null geodesics are a function of the radial position. At each radius there would be a minimum and maximum in speed of light, neither of which needs to be $c$. Any massive object will be between these speeds, but not limited to $c$. In the rotating frame the speed of light and $c$ are not the same thing.

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  • $\begingroup$ I find that topic very interesting, yet I have never seen it being covered in courses or books on special relativity. Do you have any suggestion on good literature regarding this topic (maybe especially containing your claim about minimum speed and maximum speed of massive objects as a function of the radius)? $\endgroup$
    – Octavius
    Commented Apr 23 at 11:59
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would the stationary object not appear to be moving

Here's a similar thought experiment. Imagine you have a narrowly focused, very powerful torch and shine it at the moon, so it illuminates a spot on the surface. By moving your hand, you can easily make that spot move across the surface of the moon at a speed faster than light.

However, what is really moving is the photons that fly to and from the moon at lightspeed. So nothing is going faster than light. Different photons arrive at the moon in different places, depending on the orientation of the torch.

In the same way, someone standing on the rotating body may see the other body move at great speed, but what is moving are the photons seen by the observer.

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  • $\begingroup$ I know that nothing is actually moving faster than light, but relative to the observer, could we not think of the distant object as moving faster than light? $\endgroup$
    – bbqribs2000
    Commented Apr 23 at 1:18
  • $\begingroup$ As with my lightspot, yes an observer could think it moves faster than light. $\endgroup$
    – hdhondt
    Commented Apr 23 at 1:42