arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0910.2073gr-qc
收藏

广义相对论物理解释中的群观

The group aspect in the physical interpretation of general relativity theory

Salvatore Antoci, Dierck-Ekkehard Liebscher

备注：
14 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

1915年底，爱因斯坦和希尔伯特都得到了所谓的广义相对论的场方程，他们都认为，他们的基本成就尤其需要实现一种引力理论，其基础是广义坐标变换群。爱因斯坦认为这个群论性质从物理学的观点来看是相关的，因为广义坐标允许引入参考系，而不限于可以与闵可夫斯基坐标系相关联的惯性参考系，闵可夫斯基坐标系的变换群被认为是局限于庞加莱群。然而，两年后，克雷奇曼发表了一篇论文，否定了1915年广义相对论中的群论成果的物理意义。对克雷奇曼来说，由于任何理论，无论其物理内容如何，都可以用一般协变的形式重写，所以一般坐标变换群在物理上是无关的。然而，对于使度规场自身存在的无穷小运动群，即Killing群，情况并非如此。这个群是任何给定时空理论的物理特征，因为它解释了所考虑流形的局部不变性，即，因为它的“相对论假设”。在本章中，它显示了什么后果的物理解释的一些解决方案，其相对性假设是中间的内容，当Kretschmann的立场是一贯坚持。

英文摘要：

When, at the end of the year 1915, both Einstein and Hilbert arrived at what were named the field equations of general relativity, both of them thought that their fundamental achievement entailed, inter alia, the realisation of a theory of gravitation whose underlying group was the group of general coordinate transformations. This group theoretical property was believed by Einstein to be a relevant one from a physical standpoint, because the general coordinates allowed to introduce reference frames not limited to the inertial reference frames that can be associated with the Minkowski coordinate systems, whose transformation group was perceived to be restricted to the Poincaré group. Two years later, however, Kretschmann published a paper in which the physical relevance of the group theoretical achievement in the general relativity of 1915 was denied. For Kretschmann, since any theory, whatever its physical content, can be rewritten in a generally covariant form, the group of general coordinate transformations is physically irrelevant. This is not the case, however, for the group of the infinitesimal motions that bring the metric field in itself, namely, for the Killing group. This group is physically characteristic of any given spacetime theory, since it accounts for the local invariance properties of the considered manifold, i.e., for its ``relativity postulate''. In the present chapter it is shown what are the consequences for the physical interpretation of some of these solutions whose relativity postulate is of intermediate content, when Kretschmann's standpoint is consistently adhered to.

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。

↑