The twin paradox in a cosmological context (Vol. 42, No. 5)
The twin paradox has been a source of debate since it was discovered by Einstein. It can be analytically verified assuming the existence of global nonrotating inertial frames.
The natural nonrotating frame and its identification with "fixed stars" is an aspect of Mach's Principle, which holds that the totality of matter in the universe determines the inertial frames.
Grøn and Braeck first note that the experiment by Hafele and Keating (1972), who flew atomic clocks eastward and westward around the Earth in commercial aircraft, also shows agreement with the expected result, assuming an inertial frame which is nonrotating with respect to "fixed stars." The authors then show that in the case of two observers in an otherwise empty universe (i.e., without "fixed stars") moving at different speeds on a circular path yield different twin paradox results, depending on whether one or the other – or neither – observer is assumed to be at rest.
The authors ultimately take a fresh look at the work of Brill and Cohen, who studied the geometry inside a massive rotating shell, and conclude that in the black hole limit, such a mass distribution will drag the frames around at its own rotation rate.
Taken together, and given the entire universe closely satisfying the black hole condition, this paper lends further support to the Mach Principle.
The twin paradox in a cosmological context
∅. Grøn and S. Braeck, Eur. Phys. J. Plus, 126, 79 (2011)