Yes it does, General Relativity does. It even include any accelerated frame!
And it accounts for the pseudo-forces in those frames with the existence of a gravitational potential gradient and space-time curvature. I don't think GR handles rotating frames, though.
Boosts, translations and fixed rotations relative to what??? You must consider a first basic reference frame to say that and which is it? That frame must not be accelerated to be an inertial frame but not accelerated relative to what?
I suppose the short answer is to say that there's an absolute state of
acceleration. Once you've detected an inertial reference frame (not very difficult), the Poincaré group gives you all the other reference frames with the same properties.
It must exist a basic frame or a set of frames which we could call them to be at rest! Then you after can state that any frame having a boost, translation or constant rotation relative to them is an inertial frame.
You must consider that any frame obtained by a boost, translation or constant rotation from an accelerated frame will also be an accelerated frame.
This gives absolute
acceleration. Relativity denies absolute
velocity. This, by the way, is exactly the way it was with Galilean relativity.
Just in case you didn't know, a "boost" is a transformation into a frame in relative motion. For example:
$$t' = \gamma (t - \frac{v}{c^2}x)$$
$$x' = \gamma (x - vt)$$
is a Lorentz boost along the
x-axis.
Then once we accept that "rest" frames in the Universe exist just one of them selected by some property of the universe like possible symmetry would be the "privileged" absolute frame of the Universe.
If the laws of physics are the same in an entire set of reference frames, you
cannot attribute special properties to just one.
The problem is that ages are not relative! Age is directly related to all physiological phenomena that have haened to an individual in his history.
All this tells me is that relativity is incompatible with your own worldview. A theory only contradicts itself if it predicts (in two different ways) that one observer will make two contradictory observations.
In any case, the success of relativity is due to its history of making accurate predictions. If you like, you can imagine that your mother ship is in an absolute reference frame, claim that time dilation and length contraction occur relative to that frame only, and still show that the twins will observe exactly what relativity predicts they will. In this sense, you can consider relativity to be an illusion if you want.
You cannot say something has happened if one frame of observation is selected but that thing hasn't if another one is selected!
If an event occurs in one reference frame, it occurs in all reference frames. It's only a question of when.
Suppose that in one frame of observation twin1 aged more than twin2 and so twin1 has a long bear while twin2 has not. That situation cannot change just changing the frame of observation. The fact that the twin has or not has bear cannot depend in the reference frame.
The problem here is simultaneity. Two events that occur simultaneously in one frame do not occur simultaneously in all frames. Look at the equation for the Lorentz boost I posted above. Notice that
t' is also a function of
x. Again, you can call relativity of simultaneity "real" or "apparent", but it is possible to show that either one of the moving twins will "naturally" map out a reference frame related to your mother ship frame by a Lorentz transformation.
Imagine one of the twins moving in the
+x direction at velocity
v. Suppose he wants to place a clock in front of him, and another behind him. From the point of view of the mother ship, the clock he pushes forward will move faster than
v, and so will dilate more than the twin. The clock he pushes back will move slower than
v, and so will experience less time dilation. If the clocks were synchronized before our twin moved them, they won't be synchronized afterwards. But he'll
think they're still in sync because of the difference in time it takes light to reach him from each of the clocks.