Do distant planets move faster than light relative to Earth?

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Main Question or Discussion Point

From the observation point of Earth, you can say that the sky "moves" while the Earth is still. From this point, an observer on Earth would see a distant galaxy travel a circumference millions of light years lomg around the Earth in only a day - resulting in a velocity faster than light. Special relativity says superluminal speeds are impossible so what technicality keeps this from breaking the law of physics?
 

Answers and Replies

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Drakkith
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We recognize that our frame here on Earth is a non-inertial, rotating frame of reference and thus those specific rules of SR do not apply.
 
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Drakkith
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Note that SR is based off of two postulates. From wikipedia's article on SR:
  • The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.[1]
  • The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body" (from the preface).[1] That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.
Here "inertial coordinates" means a non-accelerating system of coordinates, which excludes rotating reference frames.
 
  • #4
Mister T
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Special relativity says superluminal speeds are impossible so what technicality keeps this from breaking the law of physics?
Special relativity tells us that information cannot be transmitted at a speed faster than the speed of light in a vacuum. If, for example, you could get a particle to travel faster than this speed you could use it transmit information at this speed. Such a thing is not possible. As far as we know, according to the laws we understand.
 
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Thanks. So basically all spinning reference frames don't count, or are there any exceptions?
 
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Drakkith
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Thanks. So basically all spinning reference frames don't count, or are there any exceptions?
There are no exceptions that I know of.
 
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So basically all spinning reference frames don't count, or are there any exceptions?
Rotating coordinate systems are non-inertial, and the laws of physics need to be described differently in such systems. This is true in Newtonian physics as well. There the change consists of adding a list of "fictitious forces" (The D'Alembert, centrifugal, Coriolis, & Euler forces) that apply to all matter in the non-inertial system, depending on position and velocity. For instance, if we want to describe the sun as moving around Earth, the "force" accelerating it toward Earth is the Coriolis force, and it has to "work twice as hard" because of the centrifugal "force" pushing outward.
There is a corresponding set of rules for SR physics, but I don't know it. I assume it is very complicated and ugly. Anyway, the "no FTL" rule will not apply in its simple form.
 
  • #9
Drakkith
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I find it helpful to think about things in terms of "chasing a light beam". No matter what reference frame you are in, whether accelerating or not, nothing can ever beat a beam of light in a race. You can set up a coordinate system in a rotating frame of reference, and you'd have to account for the increasing tangential velocity that objects have the further away from you they are, but "FTL" then becomes not a single speed, but a variable speed. This makes the math extremely complicated, but in the end the result is the same. If you release an object and a beam of light from any location and send them towards any other location, nothing will every beat that beam of light. This even holds true in the expanding and curved space of General Relativity.
 

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