作为物理几何基础的变形原理
Deformation principle as a foundation of physical geometry
摘要：
物理几何学研究几何对象和点在空间或时空中的相互配置，其由距离函数$ d$或世界函数$σ=d^{2}/2$描述。提出了一种新的构造物理几何的一般方法。正确的欧几里德几何是用它的世界函数$σ_{\mathrm{E}}$来描述的。作为用$\mathcal{G}$的世界函数$σ$替换欧几里德世界函数$σ_{\mathrm{E}}$的结果，从欧几里德几何获得任何物理几何$\mathcal{G}$。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）允许人们解释量子效应，作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 $σ_{\mathrm{E}}$. Any physical geometry $\mathcal{G}$ is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function $σ_{\mathrm{E}}$ by the world function $σ$ of $\mathcal{G}$. 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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