In the new scenario, both twins are in circular orbit at different velocities around a large body, with the velocities measured by observers rotating with zero angular momentum with respect to the sky. Abramowicz and Bajtlik considered what happens when twin A stops moving, and so has a velocity of zero, and therefore a non-zero acceleration. Twin B continues to orbit at a set velocity corresponding to Keplerian free orbit and therefore has zero acceleration. Twin A is the accelerated twin, and twin B is not accelerated. As the scientists calculate, contrary to the classical version of the paradox, twin B is younger.
The scientists then considered a situation where the large body that the twins orbit decreases in mass, while the twins’ orbiting radius stays the same. Under these circumstances, twin B’s orbiting velocity no longer follows Kepler’s laws, and so he experiences an acceleration like twin A. However, the ratio of the twins’ proper times still depends only on their velocities, not on their acceleration. Since the twins’ velocities stay the same, with twin B orbiting at a larger velocity than twin A (who is not moving at all), twin B is still younger.
In the examples so far, the faster twin is younger, regardless of any acceleration. However, if the mass of the large body decreased to zero, the situation becomes the original twin paradox: twin A is not accelerated, and twin B is accelerated. In this special case, twin B is still younger - but not because he is moving faster. As the scientists explain, when the mass of the large body is zero, the explanation for the paradox changes: time dilation here is due to twin B’s acceleration, not his velocity.
“The mass causes a non-zero curvature of the spacetime, and curvature gives the spacetime a structure that defines the absolute standard of rest,” the scientists explained. “In Minkowski spacetime there are no such structures, and there is no way to tell who of the twins in moving faster in an absolute way.”