Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-03-29
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
31 pages, 10 (mostly color) figures included. revtex4. Submitted to Foundations of Physics
Scientific paper
We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim of the rotating disk, a time-lag has to be taken into account which accounts for the global anisotropy. We propose a closed Minkowski space-time as an exact equivalent to the rim of a disk, both in the rotating and non-rotating case. In this way the Sagnac effect can be explained as being purely topological, neglecting the radial acceleration altogether. This proves that the rim of the disk can be treated as an inertial system. In the same context we discuss the twin paradox and find that the standard scenario is equivalent to an unaccelerated version in a closed space-time. The closed topology leads to preferred frame effects which can be detected only globally. The relation of synchronization conventions to the measurement of lengths is discussed in the context of Ehrenfest's paradox. This leads to a confirmation of the classical arguments by Ehrenfest and Einstein.
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