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arXiv 1608.05752physics.hist-phgr-qc
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爱因斯坦如何得到他的场方程

How Einstein Got His Field Equations

Sam Walters

摘要:

我们研究了阿尔伯特·爱因斯坦1916年在《物理学年鉴》上发表的里程碑式的论文中的几页,他在论文中推导出了引力场方程。爱因斯坦做了两个启发性的和物理上有见地的步骤。第一个是以几何的方式得到真空中的场方程。第二步,从真空中的场方程出发,得到有物质存在时的场方程。(This跃迁是物理学中的基本原理,就像量子场论中的定域规范不变性原理一样。)为此,我们将快速回顾与曲线坐标、向量、张量、度量张量、Christoffel符号、黎曼曲率张量、Ricci张量有关的微分几何背景,并了解爱因斯坦如何使用几何来建模引力。

英文摘要:

We study the pages in Albert Einstein's 1916 landmark paper in the Annalen der Physik where he derived his field equations for gravity. Einstein made two heuristic and physically insightful steps. The first was to obtain the field equations in vacuum in a rather geometric fashion. The second step was obtaining the field equations in the presence of matter from the field equations in vacuum. (This transition is an essential principle in physics, much as the principle of local gauge invariance in quantum field theory.) To this end, we go over some quick differential geometric background related to curvilinear coordinates, vectors, tensors, metric tensor, Christoffel symbols, Riemann curvature tensor, Ricci tensor, and see how Einstein used geometry to model gravity.

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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