Coordinate transformation in inertial systems and hidden factor in Lorentz transformation

초록

An inertial observation system is composed of the world lines of observers moving with the same constant velocity. In contrast, the coordinate system of a single observer, which is referred to as an inertial frame, represents the world that the observer sees, and inertial frames are related by the Lorentz transformation (LT). The coordinate transformation between inertial observation systems is presented, which is derived based on the LT reformulated in a complex Euclidean space where the time components are represented by complex numbers. In the derived transformation, the one-way speed of light is anisotropic, though the two-way speed is isotropic, and absolute simultaneity is shown. In special relativity, according to the principle of relativity, inertial frames are regarded as equivalent. However, it is shown in this paper that the equivalence of inertial frames is inconsistent with the absoluteness of proper times invariant from frame to frame. There is a hidden factor in the relationship of time in LT which is not seen under the equivalence of inertial frames. The hidden factor is a correction factor which correctly makes the relationship between proper times in inertial frames. When the correction factor is taken into account, the equivalence no longer holds. The correction factor implies the existence of a preferred reference frame. The anisotropy of the space-time spaces of inertial observation systems does not mean that exact physical quantities cannot be obtained from LT. One can use LT together with the standard synchronization, but with its exact meaning, to find proper times, for example. © 2017 Physics Essays Publication.

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