Okay, my understanding of general relativity is pretty basic but...

 

If I sit in a chair on rollers with a bottle of water on a table 2 meters in front of me then spin in a complete revolution in 1 sec, by relativistic principles...

 

The bottle has traveled a distance of 2pi*r, or 12.5 meters around me at a rate of 12.5 meters/sec. Is this correct?

Not really. By moving in a circle you've undergone an acceleration, and can tell that you are the one moving.

Hmm, but I thought that from a relativistic standpoint we're both moving. Isn't there something about all coordinate systems being equal irrespective of inertial movement? (I know I probably butchered that)

Relativity allows for arbitrary coordinate systems to be used. The question whether you´re calling them equal just because you can use them all seems like a matter of taste - I´m not really sure what "equal" should or could mean in that context.

it has indeed done that relative to YOU were you to classify yourself as stationary at the time.

 

but as Swansont said, the acceleration you undergo is a dead give-away that this was clearly not the case.

The case of special relativity is that, in inertial frames of reference, nobody can claim to be moving or at rest with anything to back them up — what you call rest is arbitrary. There's no physics you can point to that will contradict someone's claim that they are at rest.

 

Now, you are free to choose any coordinate system you want, and that's not really something dictated by relativity. You generally do what's convenient. But we tend to choose an inertial frame, because then Newton's laws can be applied, and you don't have to go off and explain the strange motion of the water jug with some pseudoforce to account for the fact that it is not travelling in a straight line.

 

So yes, you can say the bottle is moving and not you. Invoking relativity is beside the point in that case. But there are really two separate issues at play here. You have to decide which one you want and which one to discard.