# Does special theory of relativity limit velocity to speed of light, but general theory not?

In fact I don't even need to spin around, just being on the spinning earth is good enough.

Suppose I look out into space at the nearest star, Alpha Centauri, approximately 4 light years away. Working from the gravity accelerated frame of reference that I occupy on the surface of the earth, th star appears to go around the earth in one day, travelling a distance of $2*\pi*4$ or roughly 24 light years - in a day.

What I am really getting at, is that relativity tells us all frames of reference are valid, as well as that things cannot travel faster than light. But from this particular frame of reference, that would not seem to be true.

This accelerated, rotating frame of reference can be described as equivalent to some other frame by general relativity, so I think it is valid to look at it from different frames of reference.

Does this imply that the theory of general relativity does not place an upper bound of the speed of light on velocity?

• Questions are free - if you want to ask two, do ask two. Please don't stuff a two questions in one. People won't notice that your second question is unanswered after I answered your first question. – MSalters Jul 28 '16 at 15:53
• Ok, I'll chop off Q2 into its own question. – user2800708 Jul 28 '16 at 15:58
• I do think that this is a good question. It is not true that only non-accelerating frames of reference are on the same footing. According to general relativity EVERY frame is on the same footing. My quick reply would be: are you sure that you can spin faster and faster, without YOU breaking the speed of light limit? – Giorgio Comitini Jul 28 '16 at 16:15
• But as you noticed, even given the usual angular speed of the Earth, the apparent velocity already exceeds the speed of light - this is why quick answers never work. – Giorgio Comitini Jul 28 '16 at 16:24
• Yes, I thought the general theory extends to accelerated frames - does this mean that the special theory implies nothing can exceed the speed of light, but that the general theory does not imply this limitation? – user2800708 Jul 28 '16 at 18:17

## 1 Answer

All non-accelerating non-rotating frames of reference are equal, so that straight away explains the apparent violation.

In general, apparent motion can easily exceed the speed of light. For instance, if I'd shine a laser on the moon, I could make that spot move over the lunar surface quite quickly simply by rotating the laser here on earth. If I rotate the laser fast enough, the spot will in fact move faster than the speed of light. This is possible because that laser light spot isn't a physical object; it's the effect of the lasers photons being reflected. And as I rotate the laser, the photons leave earth in different directions. The spot that I see move therefore consists of reflected photons, bu those are different photons over time. Each individual photon is still bound by the speed of light.