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希尔伯特的“世界方程”和他对统一科学的看法

Hilbert's 'World Equations' and His Vision of a Unified Science

Ulrich Majer, Tilman Sauer

备注：
23 pages; to appear in Einstein Studies
发表信息：
Einstein Studies Vol. 11 (2005) 259-276
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摘要：

1923年夏天，在他发表《新数学基础》一年后，也就是他的两篇《物理学基础》笔记再版的半年前，希尔伯特在汉堡发表了三部曲的演讲。在这些讲座中，希尔伯特阐述了一个异常明确的方式，他的认识论的角度对科学作为一个分支学科的所有包容科学的数学。希尔伯特思考的出发点是这样一种主张，即他1915年的原始变分公式所隐含的引力场和电磁场方程类提供了有效的候选“世界方程”，即使是考虑到外尔和爱丁顿基于仿射联络概念的统一场论的尝试。我们给出了讨论希尔伯特的讲座，特别是，检查他声称，爱因斯坦在他1923年的论文仿射统一场论只到达希尔伯特原来的1915年理论。我们也简要地评论希尔伯特的哲学观点，在这些讲座中表示。

英文摘要：

In summer 1923, a year after his lectures on the `New Foundation of Mathematics' and half a year before the republication of his two notes on the `Foundations of Physics,' Hilbert delivered a trilogy of lectures in Hamburg. In these lectures, Hilbert expounds in an unusually explicit manner his epistemological perspective on science as a subdiscipline of an all embracing science of mathematics. The starting point of Hilbert's considerations is the claim that the class of gravitational and electromagnetic field equations implied by his original variational formulation of 1915 provides valid candidate `world equations,' even in view of attempts at unified field theories á la Weyl and Eddington based on the concept of the affine connection. We give a discussion of Hilbert's lectures and, in particular, examine his claim that Einstein in his 1923 papers on affine unified field theory only arrived at Hilbert's original 1915 theory. We also briefly comment on Hilbert's philosophical viewpoints expressed in these lectures.

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