﻿ 四元数四维间隔不变性和时空坐标变换

# 四元数四维间隔不变性和时空坐标变换Quaternion, Invariance of 4-Dimensional Interval and Transformations of Spacetime Coordinates

By the use of quaternion, the transformations of space-time coordinates in special relativity are studied. 1) The general transformations in quaternion form are derived, which preserve the invariance of 4-dimensional interval, and it is found that the invariance of the interval can not determine the Lorentz transformation uniquely. 2) Based on the con-dition that preserves the invariance of time, the general transformations reduce to the first kind of special transforma-tions, in which the space rotations are included. 3) Based on the condition that preserves the invariance of a space coor-dinate, the general transformations reduce to the second kind of special transformations, in which the proper Lorentz transformations are included. It is pointed out that the quaternion form of Lorentz transformations in some literatures should be amended. 4) From the general transformations in quaternion form, two types of new transformations are introduced, which are discrete transformations, including identical, reflection and transposition ones, and unilateral transformations. These new transformations are different from the traditional space rotations and the normal Lorentz transformations.

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