管状几何结构作为时空概念新修正的原因
Tubular geometry construction as a reason for new revision of the space-time conception
摘要：
管状几何（T-几何）是一个推广的正常欧几里德几何，建立在性质的sigma-immanence。正确的欧几里得几何可以完全用世界函数$σ=ρ^{2}/2$来描述，其中$ρ$是距离。这个属性被称为sigma-immanence。假设任何物理几何都是σ-不变量的，则在欧氏几何的σ-不变量表示中，用$σ$代替欧氏世界函数$σ_{E}$，得到T-几何$\mathcal{G}$.我们得到T几何$\mathcal{G}$，由世界函数$σ$描述。这种几何构造方法简单有效。T-几何具有一个新的几何性质：几何的非退化性。用单参数函数的形式描述了齐次各向同性T-几何类。用T-几何作为时空几何，可以构造自由粒子和几何化粒子质量的原随机运动的确定性时空几何。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）。粒子质量的几何化似乎与直线段的有限可分性有关。基本粒子质量谱问题与其说是动力学问题，不如说是几何学问题，这种说法是粒子质量几何化的必然结果。
英文摘要：
The tubular geometry (T-geometry) is a generalization of the proper Euclidean geometry, founded on the property of sigma-immanence. The proper Euclidean geometry can be described completely in terms of the world function $σ=ρ^{2}/2$, where $ρ$ is the distance. This property is called the sigma-immanence. Supposing that any physical geometry is sigma-immanent, one obtains the T-geometry $\mathcal{G}$, replacing the Euclidean world function $σ_{E}$ by means of $σ$ in the sigma-immanent presentation of the Euclidean geometry. One obtains the T-geometry $\mathcal{G}$, described by the world function $σ$. This method of the geometry construction is very simple and effective. T-geometry has a new geometric property: nondegeneracy of geometry. The class of homogeneous isotropic T-geometries is described by a form of a function of one parameter. Using T-geometry as the space-time geometry one can construct the 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). Geometrization of the particle mass appears to be connected with the restricted divisibility of the straight line segments. The statement, that the problem of the elementary particle mass spectrum is rather a problem of geometry, than that of dynamics, is a corollary of the particle mass geometrization.
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