标题： 爱因斯坦的物理策略、能量守恒、对称性和稳定性：“但格罗斯曼和我相信守恒定律不成立” 显示英文标题

标题： Einstein's Physical Strategy, Energy Conservation, Symmetries, and Stability: "but Grossmann & I believed that the conservation laws were not satisfied"

摘要： 最近由Renn、Sauer、Janssen等人对广义相对论历史的研究显示，爱因斯坦部分地通过包括牛顿极限、电磁类比和能量守恒的物理策略找到了他的场方程。这些主题后来也被粒子物理学家使用。爱因斯坦的物理策略和粒子物理学的推导有何异同？他使用了哪些能动量复式，为什么？爱因斯坦是否将守恒与对称性联系起来，如果是的话，是哪种对称性？爱因斯坦使用了一个从他假设的线性坐标协变x'= Mx得出的恒等式来将其与规范张量联系起来。通常他避免使用物质欧拉-拉格朗日方程，因此没有很好地处于使用或重新发明Herglotz-Mie-Born理解的状态，即规范张量由于平移对称性而守恒，这一结果源于拉格朗日、哈密顿和雅可比的工作。相比之下，Mie和Born关注规范张量的不对称性，而爱因斯坦不需要担心，因为他的Entwurf拉格朗日量更多地基于标量理论而非麦克斯韦理论。因此，它也有3个幽灵，未能通过20世纪20年代到30年代的先验粒子物理稳定性测试，该测试在拉格朗日和狄利克雷的稳定性工作中已有先例。对Entwurf理论的批评可以与爱因斯坦1915年对Entwurf理论的批评相比较，当时他认为该理论不接受旋转坐标且未能正确计算水星近日点进动。粒子物理也可以在引力和时空的历史编纂中发挥作用。这个话题可以作为科学史中最近重新考虑的现时主义、辉格主义等问题的一个有用案例研究。 显示英文摘要

摘要： Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. As a result, it also has 3 ghosts, failing a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. Particle physics also can be useful in the historiography of gravity and space-time. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like.