The twin paradox and the principle of relativity

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: 1. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation; 2. Perfect dragging in an exact solution of Einstein's field equations describing flat spacetime inside a shell with Kerr spacetime outside it; 3. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.

A relativistic trolley paradox

“…1 Such efforts have been useful, as analyzing seemingly paradoxical situations usually leads to a more detailed understanding of relativistic kinematics. [2][3][4][5][6][7][8][9][10][11][12][13] We here present a new special relativistic "paradox." The situation involves a combination of translational and rotating motion-the translational motion of a trolley and the rotational motion of its wheels.…”

A source of the C-metric with perfect translational inertial dragging

“…The main point is that a shell of matter is only an idealized model for a Universe with lookback distance equal to the Schwarzschild radius of the mass inside this distance [21,22]. One does not need this static model to behave perfectly well in this limit since this model is not realized in nature.…”

The Real Cause of Differential Aging in the Twin “paradox”

“…The physicists have employed various approaches, such as space-time diagram [1]- [2], special relativity [3]- [10], acceleration and gravity calculus [11]- [20], radar time [21], circular [22], and Doppler effect [23]- [24], etc., to solve the "paradox" and offered a consistent conclusion that the traveler twin is younger than the homebody twin on the Earth. However, some authors attribute the cause of differential aging to acceleration [11,12,14,15,17,20,21], while others believe that accelerations should not be regarded as the source of differential aging, but frame switch is [1,9,18]. So far there is no agreement on this issue.…”