物理几何基础形变原理及其在时空几何中的应用
Deformation principle as foundation of physical geometry and its application to space-time geometry
摘要：
物理几何学研究几何物体和点在空间或时空中的相互配置，这是由距离函数d或世界函数σ=d^{2}/2描述的。提出了一种新的构造物理几何的一般方法。用世界函数σ_E描述了真欧几里德几何.任何一个物理几何G都是由欧氏几何G的世界函数σ代替欧氏几何的世界函数σ_E而得到的。该方法简单有效。它引入了一个新的几何性质：几何的非退化性。利用这种方法，人们可以用自由粒子和几何化粒子质量的原始随机运动来构造确定性的时空几何。这样一种定义恰当的时空几何（以量子常数作为几何的一个属性）允许人们将量子效应解释为随机粒子运动的统计描述的结果（不使用量子原理）。
英文摘要：
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function σ=d^{2}/2. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function σ_E. Any physical geometry G is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function σ_E by the world function σof G. This method is very simple and effective. It introduces a new geometric property: nondegeneracy of geometry. Using this method, one can construct deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles).
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