Authors: Yang-Ho Choi
The Sagnac effect could not have been exactly explained with consistency under the theory of special relativity (TSR). The conundrum of TSR has been completely solved fully in the relativistic context. Special relativity is reformulated without the postulates of the relativity principle and the light velocity constancy, employing a complex Euclidean space (CES), which is an extension of Euclidean space from the real number to the complex number. In the reformulation, the relativity in the representation and the light velocity constancy are obtained as properties that isotropic space-time spaces have. The coordinate systems each have perpendicular axes in CES and the relativistic transformation has the form of rotation. These characteristics of the formulation pave the way for the relativistic approach to circular motion. The relativistic transformation from the inertial frame to the circular frame is shown to have the same representation as that from the circular to the inertial, which implies that circular motions can be described relative to linear motions and vice versa. The difference between the arrival times of two light beams in the Sagnac experiment can be exactly found by the circular approach presented, which shows that the non-relativistic and relativistic analysis results are the same within a first order approximation. The circular approach can also be applied to the analysis of the Hafele–Keating (HK) experiment. The analysis of Hafele and Keating appears to exploit the results of this paper, though circular motions were treated as liner motions. The relativistic approach for circular motion, which is formulated without any postulates, can lead to propound understanding of relativity and true space-time spaces. These issues are examined.
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[v1] 2014-10-28 10:22:16
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