多元性作为微观世界的一个重要属性
Multivariance as a crucial property of microcosm
摘要：
广义几何构造的传统方法是根据公理推导出几何的所有命题，在这个意义上说，这种方法似乎是不完善的，多元几何不能用这种方法来构造。多元几何是这样一种几何，其中在点P处有许多向量PP '，PP“，.它们等价于点Q处的矢量QQ'，但它们之间不等价。在传统的（欧几里德）方法中，等价关系是传递的，而在多元几何中，等价关系一般是不传递的。这就是为什么多元几何不能从公理系统中推导出来的原因。微观世界的时空几何是多元的。多元几何是一种粒状几何，即部分连续部分离散的几何。多元分析是一种粒度描述的数学方法。时空几何的颗粒性（和多元性）产生了微观世界中粒子的多元（量子）运动。此外，粒状时空产生了一些鉴别机制，负责离散参数（质量，电荷，自旋）的基本粒子。粒子的动力学似乎完全由粒状时空几何的性质决定。量子原理似乎是不必要的。
英文摘要：
The conventional method of a generalized geometry construction, based on deduction of all propositions of the geometry from axioms, appears to be imperfect in the sense, that multivariant geometries cannot be constructed by means of this method. Multivariant geometry is such a geometry, where at the point P there are many vectors PP', PP'',... which are equivalent to the vector QQ' at the point Q, but they are not equivalent between themselves. In the conventional (Euclidean) method the equivalence relation is transitive, whereas in a multivariant geometry the equivalence relation is intransitive, in general. It is a reason, why the multivariant geometries cannot be deduced from a system of axioms. The space-time geometry in microcosm is multivariant. Multivariant geometry is a grainy geometry, i.e. the geometry, which is partly continuous and partly discrete. Multivariance is a mathematical method of the graininess description. The graininess (and multivariance) of the space-time geometry generates a multivariant (quantum) motion of particles in microcosm. Besides, the grainy space-time generates some discrimination mechanism, responsible for discrete parameters (mass, charge, spin) of elementary particles. Dynamics of particles appears to be determined completely by properties of the grainy space-time geometry. The quantum principles appear to be needless.
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