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arXiv physics/0207065physics.gen-ph
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狭义相对论中的参考空间:一种内禀方法

Reference spaces in Special Relativity Theory: an intrinsic approach

Nilo C. Bobillo-Ares, Carlos Dehesa-Martinez

摘要:

从爱因斯坦关于空间概念的构建的建议开始,我们详细阐述了一种内在的方法来获得两个惯性参考空间之间的空间和时间变换,数学建模为仿射欧氏空间。为了把两个空间的空间读数联系起来,所采用的主要手段是所谓的示踪映射,它把一个空间的快照映射到另一个空间上。空间和时间变换的一般形式是作为一个仿射-保持映射兼容的相对性原理,一个圆柱对称的空间之间的相对速度和群字符的转换。在得到伽利略变换和洛伦兹变换之后,同样的方法被应用于两个经典问题:牛顿力学的科里奥利定理和狭义相对论中旋转圆盘的几何。即使在牛顿力学的情况下,区分参考空间的可能性也是有用的。

英文摘要:

Starting from a suggestion of Einstein on the construction of the concept of space, we elaborate an intrinsic method to obtain space and time transformations between two inertial spaces of reference, mathematically modeled as affine euclidean spaces. The principal device introduced for relating the space readings in both spaces is the so-called tracer mapping, which makes a snapshot of a space onto the other. The general form of the space and time transformations is obtained as an affine--preserving mapping compatible with the principle of relativity, a cylindrical symmetry around the relative velocities between spaces and the group character of the transformations. After having obtained Galileo and Lorentz transformations, the same method has been applied to two classical problems: the Coriolis theorem of Newtonian Mechanics and the geometry of a rotating disk in Special Relativity. Even in the case of Newtonian Mechanics, the possibility of distinguishing the spaces of reference is found useful.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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