Fixed Stars Moving Faster Than Light? Problem?

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Discussion Overview

The discussion revolves around the perception of fixed stars appearing to move faster than light due to the observer's rotation. Participants explore the implications of this observation on the cosmic speed limit and the nature of relative motion, touching on concepts from special and general relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that when spinning in an open field, stars appear to move faster than light relative to the observer, questioning if this breaks the cosmic speed limit.
  • Another participant clarifies that the observer's rotating frame is not an inertial frame, suggesting that the coordinate speed of light is limited only in inertial frames.
  • It is proposed that the physical relative velocity between two objects remains bounded by the speed of light, regardless of the coordinate system used.
  • Discussion includes the complexity introduced by using non-inertial frames or complex coordinate systems, which can obscure the invariance of light speed.
  • A participant expresses interest in whether the concept of local speeds being limited to c is discussed in well-known texts, referencing authors like Carroll and Wald.
  • Another participant mentions that in curved spacetime, comparing velocities at different points can be ambiguous, reinforcing that local relative speeds cannot exceed c.
  • It is suggested that using simpler coordinate systems, like Cartesian coordinates, is often more straightforward than complex ones, especially in the context of special relativity.

Areas of Agreement / Disagreement

Participants express differing views on the implications of rotating frames and coordinate systems on the perception of speed, with no consensus reached on the nature of relative motion in this context.

Contextual Notes

The discussion highlights limitations in defining relative speeds in non-inertial frames and the potential complications arising from the choice of coordinate systems, without resolving these complexities.

KingSnackMan
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If I spin around in an open field at night and look up to the stars they appear to be moving relative to me. Additionally, they are very far away and trace out a giant arc length in a very short time (S=rθ). With respect to me, these stars are moving faster than light. Is this a problem? Has the cosmic speed limit been broken? Do I have to abandon relative motion?
 
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To summarise, your rotating frame is not an inertial frame. The coordinate speed of light is only limited and fixed in inertial frames.

The physical relative velocity between two objects is a different matter. It is bounded by c regardless of the coordinates you use. It also gets slightly more complicated in GR.
 
The speed of light is invariant and cannot be exceeded locally. If you use a simple Cartesian coordinate system then this concept is simple to express everywhere just by dropping the word "locally" (at least for SR).

If you use a more complex coordinate system, such as rotating polar coordinates, then this concept is not simple to express in general. You find that the speed of light expressed in these coordinates is different at different points and in different directions. However, all the additional complexity is down to a silly choice of coordinates. You are still expressing the same notion of the invariance of light speed, just hiding the invariance behind a layer of complicated maths.

There can be good reasons to do this (see GR for one). But don't if you don't have to, would be my advice.
 
This is very interesting, specifically that it is only local speeds that need to be c. Is this in any well known books? Carroll? Wald?
 
Any text covering general relativity will mention it, I should imagine. In curved spacetime it isn't necessarily possible to make an unambiguous comparison of velocities (or any other vector) at one point with velocity (or whatever) at another point. So you can only insist that local relative speeds cannot exceed c bcause you can't really define relative speed between spatially separated objects.

You can define relative speed for spatially separated objects in flat spacetime (i.e. in special relativity), and hence insist that it must be less than c. If you choose a complicated set of coordinates, you can hide that simple statement quite thoroughly.
 
Let me add that this is very similar to using curvilinear coordinates. Unless you have a special reason not to, using Cartesian coordinates is almost always the easiest. In the same fashion, using Minkowski coordinates in SR is most often the easiest.
 

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