Relativistic Paradox of a Uniformly Charged Sphere Moving with Constant Velocity

A magneto-electric field appearing in a laboratory due to moving charges has unusual properties. In particular, such a field of kinematical origin does not obey the wave equation with a non-relativistic velocity instead of light speed;so, its movement resembles that of a rigid body. In this paper the field of a uniformly charged sphere moving at constant velocity is considered. Relativistic axiom, implicitly used in the derivation of formulas describing a kinematic deformation for the proper spherical field from the point of view of a fixed observer, is revealed. A discrepancy was found between the generally accepted idea of the configuration of a deformed field and its real geometry. It is shown that the correct interpretation of known formulas leads to a logical contradiction, which cannot be eliminated within the framework of the theory of relativity. A scheme of a decisive experiment is proposed.

论希尔伯特几何公理的综合性质

受时代局限,康德基于欧氏几何宣称几何命题的先天综合性质。欧氏几何的现代数学表达为希尔伯特几何公理系统,并且后者可以方便地演化出非欧几何。于是,论证希尔伯特几何公理的先天综合性质可以在现代数学的背景中为一般几何命题的先天综合性质提供支持。希尔伯特几何公理的先天性不言而喻。继反驳石里克对希尔伯特几何系统的公理定义所作的分析性论证之后,对希尔伯特几何公理的综合性质的正面论证在于,阐明蕴涵定义超出分析性程序的方法论本质,揭示希尔伯特几何公理对业已被证明为先天综合知识的算术的双重依赖,并利用多种几何并存的局面展示享有唯一性地位的算术系统所不能彰显的先天综合知识的独特模态。