空间计量中长度单位和距离测量

长度单位定义是建立在光直线传播、光速在真空中为常数，以及光速各向同性的理论基础上，二维球面上的直线，在三维空间中是弯曲的测地线；三维空间的直线，在四维时空中也是弯曲的测地线。长度单位的定义是否适用四维时空呢？SI秒和SI米的定义适用于全域时空，但使用它们必需明确原时和坐标时的区别。爱因斯坦的狭义相对论以及光速不变原理只适用于惯性系，不适用于非惯性系。本文以转盘上的非惯性坐标系为例，利用广义相对论的坐标变换和时空度规运算，揭示了非惯性坐标系上的时空弯曲和光的非直线传播现象。计算了非惯性坐标系上Sagnac效应对卫星和地面站双向测距的影响，初步研究表明空间测量范围从局域推广到全域的话，诸如引力红移、相对速度效应、Sagnac效应等将会成为空间长度测量不确定度的影响因素，因此空间计量理论必须建立在广义相对论基础之上，用四维时空观念理解空间距离测量问题。

Length Unit and Distance Measurement in Space Metrology

The definition of length unit is found on the theory that light goes straight, light speed is constant in vac?uum, and light velocity is isotropy. The straight-line of 2-Dimension on sphere is looked like curve geodesic in space of 3-Dimension; and the straight-line in 3-D space is also curve geodesic in 4-D space-time. However, whether this definition is suitable for 4-D space-time or not? The definition of SI second and SI meter is the same with whole global space-time,but we must clear the difference between proper time and coordinate time when we use them. Einstein’s Special Relativity theory and the principle of light speed constant are only used on inertial-system, cannot be used on non-inertial-system.For example on non-inertial-system of rotation plate, we use coordinate transfer and calculation of space-time metric by GR to realize the phenomenon that space-time is curve and light goes non-straight path. For example to measure distancebetween satellite and earth-station, we calculate a special case of Sagnac Effect on non-inertial-system. Brief research show that range of distance extend from local to large area in space, these effects such as relative velocity, gravity red-shift and Sagnac, will become important influence factor of uncertainty of measuring distance. So the theory of Space Metrologymust be found on the theory of General Relativity（GR）, and take the viewpoint of space-time on 4-Dimension to under?stand the problem of distance measurement.