>If you google search, you will find me explaining that Einstein >claimed to have solved GRT's clock paradox. ;-)
The use of GR to explain the results of the twin paradox is a little perverse, because GR is a generalization of SR. In the case of empty space far from any large gravitating bodies, GR reduces to SR, so any GR solution to the twin paradox would have to have already been a solution in SR. Which is exactly the case: GR solves the twin paradox in the exact way that SR does.
Many people are confused by the equivalence principle into thinking that Einstein's theory of gravity is necessary in order to describe physics from the point of view of an accelerating coordinate system. That's exactly backwards. The reasoning goes the other way around:
1. We already understand SR as described in standard inertial coordinates (the type of coordinate systems related by the Lorentz Transformations).
2. We use ordinary calculus to figure out what SR looks like in other coordinate systems. This is not a different *physical* theory than SR, any more than using spherical coordinates to do Newtonian mechanics means we are no longer doing Newtonian mechanics.
3. Using calculus, we can figure out what SR looks like in an accelerated coordinate system (a coordinate system in which an accelerated observer is "at rest". What we find is that, as measured in such a coordinate system, a clock shows an elapsed time T such that dT/dt is position dependent: Clocks that are "higher" (in the direction of the acceleration) run faster, and clocks that are "lower" run slower.
4. Now, we invoke the equivalence principle, and assume that the situation of being at rest in a uniform gravitational field is approximately the same as being at rest in an accelerated coordinate system in SR.
5. We conclude from 4 that clocks that are stationary and "higher" in a gravitational field run faster than clocks that are stationary and "lower". So a clock high on a mountain runs faster than a clock at sea level (after accounting for the SR effect of velocity due to the rotating Earth).
The equivalence principle allows us to *approximately* solve problems involving gravity by using SR. That's what it's useful for. The other way around, using GR to solve problems that involve acceleration in flat spacetime, makes little sense, because you don't need GR. You just need SR + calculus.