Abstract:
In the standard formulation of the twin paradox an accelerated twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation. Perfect dragging in an exact solution of Einsteins field equations describing flat spacetime inside a shell with Kerr spacetime outside it. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.

Abstract:
After pointing out the historical avatar at the origin of a would be twin or clock paradox, we argue that, at least on a local scale, the (re-qualified) paradox is but a necessary consequence of the sole principle of causality.

Abstract:
It is shown that the "twin paradox" arises from comparing unlike entities, namely perceived intervals with eigenintervals. When this lacuna is closed, it is seen that there is no twin paradox and that eigentime can serve as the independent variable for mechanics in Special Relativity.

Abstract:
The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.

Abstract:
The accepted resolution of the twin paradox in relativity states that the age of the inertial twin `jumps' when the traveling twin undergoes his turn-around acceleration. This resolution is based on the use of the equivalent gravitational shift in the frame of the accelerating twin. We use the same analysis to propose a symmetric variant of the problem with the twins experiencing identical acceleration and deceleration phases, but which predicts conflicting results for the age of the other twin. We also propose an unambiguous test of the standard resolution based on the Pound-Rebka experiment.

Abstract:
In principle, the twin paradox offers the possibility to go on a trip to the center of our galaxy or even to the end of our universe within life time. In order to be a most comfortable journey the voyaging twin accelerates with Earth's gravity. We developed some Java applets to visualize what both twins could really measure, namely time signals and light coming from the surrounding sky.

Abstract:
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy results only from faulty assumptions in the transition from one reference system to another. The twin paradox does not exist. But the Lorentz invariance of the theory has strong consequences, if we assume that it is valid not only locally, but also on cosmic scale.

Abstract:
The twin paradox is the best known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than a twin who stayed on Earth. This result appears puzzling, since the situation seems symmetrical, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence it is called a "paradox". In fact, there is no contradiction and the apparent paradox has a simple resolution in Special Relativity with infinite flat space. In General Relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of spacetime and the limitations of the equivalence between inertial reference frames.

Abstract:
We consider a new version of the twin paradox. The twins move along the same circular free photon path around the Schwarzschild center. In this case, despite their different velocities, all twins have the same non-zero acceleration. On the circular photon path, the symmetry between the twins situations is broken not by acceleration (as it is in the case of the classic twin paradox), but by the existence of an absolute standard of rest (timelike Killing vector). The twin with the higher velocity with respect to the standard of rest is younger on reunion. This closely resembles the case of periodic motions in compact (non-trivial topology) 3-D space recently considered in the context of the twin paradox by Barrow and Levin, except that there accelerations of all twins were equal to zero, and that in the case considered here, the 3-D space has trivial topology.

Abstract:
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a non-vanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.