# Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation:

A space station modeled as a ring in free space is rotating about its centre point at a high speed.

I am trying to work out where time flows slower. From general relativity, I have stated that the centrifugal acceleration at the ring is greater than at the centre (which is 0) and so the can be thought of as the lowest point of the gravitational field (strongest feeling of gravitational acceleration). So time on the ring flows slower than at the centre (from Einsten).

However, I can see that there may be another reason. Special relativity states (assuming its two assumptions are held) that a moving clock runs slower than one which is stationary. Okay, so in this case I can also say that the clock on the ring is slower, because it is moving faster than the one at the centre. But then I have a problem: a person on the ring may think that he is stationary and the person at the centre is spinning around (so has angular velocity) and it is his clock which is moving slower. Of course, that would be the end of it, and time is not absolute yada yada yada. However, in this case the first assumption of special relativity is broken, both of these frames are not inertial frames of references; the ring is 'feeling' an acceleration. In this case, I have been told that special relativity cannot be applied, but is this true. From this, the person on the ring can now tell that it is definitely he who is moving, not the person at the centre of the ring and so there is no problem here: it is obvious that the clock on the ring shows that time flows slower than at the center. Is this a valid statement to make? If it is, then how much slower is time flowing due to SR? Am I able to use the $t' = \gamma t$ formula as usual ($t'$ is the time for the clock at the centre)? If I am, then why? As far as I am aware SR should not hold if the frames are not inertial.

• I'm pretty sure you can work with special relativity just fine, even when observers are not in inertial frames. – Danu Mar 28 '14 at 8:17
• – John Rennie Mar 28 '14 at 9:54
• Keir, the duplicate I've suggested isn't at first glance an obvious duplicate, but it does explain how to treat a similar system of a planet rotating round a star. – John Rennie Mar 28 '14 at 9:59
• Keir, the short answer is yes. The problem with using SR for noninertial frames is that you need to do an infinite number of Lorentz transformations. As you can imagine, this is not practically or computationally feasible. – honeste_vivere Oct 23 '14 at 21:19