We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not essential. Next we consider the quantum setting, where the conceptual problems of the standard formalism obstruct a rigorous analysis of the issue. We then analyze the fate of energy conservation within the various viable paths to address such conceptual problems; in all cases we find no satisfactory way to define a (useful) notion of energy that is generically conserved. Finally, we focus on the implications of this for the semiclassical gravity program and conclude that Einstein's equations cannot be said to always hold.

中文翻译：

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关于守恒律在物理学中的地位：对半经典引力的影响

我们首先考察基本保护法思想的历史，并简要考察保护法在不同古典背景下的作用。在这种情况下，我们发现保护法是有用的，但往往不是必需的。接下来，我们考虑量子环境，其中标准形式主义的概念性问题阻碍了对该问题的严格分析。然后，我们分析各种可行途径中节能的命运，以解决此类概念性问题；在所有情况下，我们都找不到令人满意的方法来定义通常守恒的（有用的）能量概念。最后，我们将重点放在半经典重力程序的含义上，并得出结论，不能说爱因斯坦方程始终成立。