论规范引力对几何三位一体的“超动量挑战”
On Gauge Gravity's 'Hypermomentum Challenge' to the Geometric Trinity
- Lichtenberg Group for History and Philosophy of Physics, Institute of Philosophy, University of Bonn（波恩大学哲学研究所利希滕贝格历史与物理哲学小组）
- Argelander Institute for Astrophysics, University of Bonn（波恩大学阿根兰德天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文比较广义相对论与挠率、非度量性重构的等价性主张同规范引力传统的冲突，指出等价性仅在物质不耦合独立仿射联络时成立，选择取决于简约性权衡。
AI中文摘要：
关于广义相对论与其两种重构形式之间存在动力学等价性的主张，其中引力分别编码在挠率和非度量性中，已引起一些关注。若此“几何三位一体”成立，则意味着即使在原则上也无法确定一个人所栖居的时空解是否具有曲率、挠率或非度量性（就几何探针是测试粒子的路径而言）。这一主张与长期以来将引力作为规范理论研究的传统直接冲突，在该传统中，不同的几何属性耦合于物质的不同属性（如能量-动量耦合于曲率，自旋角动量耦合于挠率）。在这篇短文中，我比较了这两种对时空几何化的相互冲突的框架，并描述了它们分歧的确切来源、性质及影响。等价性主张仅在物质部分受到实质性限制时才成立，即物质不耦合于独立的仿射联络。由于相关耦合仍超出当前实验可及范围，框架之间的选择取决于本体论、认识论和方法论形式的简约性之间的权衡。
英文摘要：
Claims concerning a dynamical equivalence between general relativity and two reformulations of it, in which gravity is encoded in torsion and non-metricity respectively, have attracted some attention. If taken to be true, this 'Geometric Trinity' suggests that it is impossible to determine, even in principle, whether one inhabits a spacetime solution possessing curvature, torsion or non-metricity (insofar as the probes of geometry are paths of test particles). This claim is in direct tension with the long tradition of studying gravity as a gauge theory, in which distinct geometric attributes couple to distinct properties of matter (such as energy-momentum to curvature and spin angular momentum to torsion). In this short paper, I compare these two conflicting frameworks for geometrizing spacetime and describe the precise source, nature and implications of their disagreement. The equivalence claim holds only under a substantive restriction on the matter sector, namely that matter does not couple to an independent affine connection. Because the relevant couplings remain beyond current empirical reach, the choice between the frameworks turns on a trade-off among ontological, epistemic, and methodological forms of parsimony.
