物理学中物质运动的几何不变量
Geometrical Invariants of Matter Motion in Physics
摘要：
本文定义了带有观测者的时空几何为真空几何（它定义了理想的物理测量几何），定义了带有物质的时空几何为时空几何。以附着有物质的初始时空几何为参考几何（称为初始共动坐标系），由初始时空几何中测量的四维位移场确定附着有物质的当前时空几何（称为当前共动坐标系）。物质运动由四维坐标系中基本矢量的运动变换表示。用位移表示的运动变换描述了物质运动的瞬态几何形式。在广义相对论和规范场中，字线距离的几何不变量被用来定义时空连续体的几何。然而，根据这项研究，这是正确的，只有当时间转移是在特殊的形式。对于更复杂的物质运动，规范场和广义相对论都将失效。本文指出，传统的物理守恒定律以及规范场和广义相对论引入的几何不变量都是有限几何场论的简单特例。
英文摘要：
This paper defines the spacetime geometry attached with observor as vacuum geometry (it defines the idea physical measurement geometry) and the spacetime geometry attached with matter as spacetime geometry. The initial spacetime geometry attached with matter is taken as refference geometry (named as initial co-moving coordinator system), and the current spacetime geometry attached with matter (named as current co-moving coordinator system) is determined by the four-dimensional displacement field measured in initial spacetime geometry. Matter motion is expressed by the motion transformation of basic vectors of four-dimensional co-moving coordinator system. The transformation of motion expressed by displacement describes the transient geometry form of matter motion. In general relativity theory and in gauge field theory, the geometrical invariant of word-line distance is used to define the geometry of space-time continuum. However, based on this research, this is only true when the time-shift is in special form. For more complicated matter motion, the gauge field theory and general relativity will be failed. The paper shows that traditional physical conservation laws and the geometrical invariant introduced by the gauge field theory and general relativity are included in the finite geometrical field theory as simple special cases.
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