爱因斯坦与希尔伯特：广义相对论的创立

发现的相对性：希尔伯特关于物理学基础的第一个注释

The Relativity of Discovery: Hilbert's First Note on the Foundations of Physics

希尔伯特关于“物理学基础（第一次通信）”的论文，现在主要是因为它平行发表了基本上相同的广义相对论的引力场方程，爱因斯坦在五天后，即1915年11月25日发表了一篇关于“引力场方程”的笔记。此外，希尔伯特和爱因斯坦在1915年11月这一关键月份的密切通信，使历史学家面临着一个平行研究的案例，以及重建当时希尔伯特和爱因斯坦之间相互作用的相关问题。以前对这些问题的评估最近受到了Leo Corry，Jürgen Renn和John Stachel的挑战，他们提请注意迄今为止未被注意的希尔伯特注释的第一组证明。这些证据承担印刷厂的邮票12月6日和显示实质性的差异，以公布的版本。通过关注这些发现对于重建爱因斯坦通向广义相对论的道路的影响，关于希尔伯特在这一事件中的作用的一些问题仍然是开放的。希尔伯特对爱因斯坦的反应有多大？希尔伯特在他的笔记中所关注的研究是什么？在1915年秋天，这些研究是如何与爱因斯坦的研究在某种程度上重叠的？希尔伯特和爱因斯坦当时是如何看待对方以及他们同时进行的活动的？希尔伯特希望达到什么目的？他究竟达到了什么目的？带着这些问题，我在本文中讨论了希尔伯特关于“物理学基础”的第一个注释，它的史前史和特征，而且，为了启发性的目的，我主要是从希尔伯特的角度来讨论的。

Relativity and Equivalence in Hilbert Space: A Principle-Theory Approach to the Aharonov-Bohm Effect

This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.

Emmy Noether on Energy Conservation in General Relativity

During the First World War, the status of energy conservation in general relativity was one of the most hotly debated questions surrounding Einstein's new theory of gravitation. His approach to this aspect of general relativity differed sharply from another set forth by Hilbert, even though the latter conjectured in 1916 that both theories were probably equivalent. Rather than pursue this question himself, Hilbert chose to charge Emmy Noether with the task of probing the mathematical foundations of these two theories. Indirect references to her results came out two years later when Klein began…

Relativity Theory Refounded

We put forward a new view of relativity theory that makes the existence of a flow of time compatible with the four-dimensional block universe. To this end, we apply the creation-discovery view elaborated for quantum mechanics to relativity theory and in such a way that time and space become creations instead of discoveries and an underlying non-temporal and non-spatial reality comes into existence. We study the nature of this underlying non-temporal and non-spatial reality and reinterpret many aspects of the theory within this new view. We show that data of relativistic measurements are suffic…

Did Einstein "Nostrify" Hilbert's Final Form of the Field Equations for General Relativity?

Einstein's biographer Albrecht Fölsing explained: Einstein presented his field equations on November 25, 1915, but six days earlier, on November 20, Hilbert had derived the identical field equations for which Einstein had been searching such a long time. On November 18 Hilbert had sent Einstein a letter with a certain draft, and Fölsing asked about this possible draft: "Could Einstein, casting his eye over this paper, have discovered the term which was still lacking in his own equations, and thus 'nostrified' Hilbert?" Historical evidence support a scenario according to which Einstein discover…

关于广义相对论变分原理的一个奇怪细节

A Strange Detail Concerning the Variational Principle of General Relativity Theory

由于对广义相对论的变分原理作了一个不必要的形式假设，使爱因斯坦和希尔伯特感到困惑，从而引起了数学上的复杂性。一些历史上的混乱似乎是由于不可能直接在那里使用传统的欧拉-拉格朗日形式主义造成的，即使这样，它也只不过是应用最小作用量原理的各种可能程序之一。相应地，到目前为止，在文献中没有任何直接计算，只有部分的数值修改-明确考虑到希尔伯特曾经提到过没有实现-将允许从这些作者的初始公式计算基本爱因斯坦张量密度，这不能从字面上理解。然而，坚持一个仅仅是象征性的欧拉-拉格朗日形式主义，这需要一个明确的区分“分量微分”和“张量微分”定义在这里。各种相应的解决方案，包括可能最自然的。其中两项在本说明电子版所附的详细补充材料中得到进一步核实。