Abstract The paper re-examines Nordstrom's scalar theory of gravity (NG) – arguably the most convincing relativistic theory of gravity before the advent of General Relativity. It exists in two different formulations. In Nordstrom's original one (1913), NG appears to describe a scalar gravitational field on Minkowski spacetime. In Einstein and Fokker’s (1914) version, NG seems to be a spacetime theory: It reconceptualises gravitational effects as manifestations of non-Minkowskian inertial structure. Both variants of NG give rise to three contradictory verdicts on the status and validity of fundamental principles: the Weak Equivalence Principle, the existence of gravitational energy, and energy conservation. Given the putative equivalence of both variants of NG, this ambiguity seems paradoxical to the spacetime realist. I'll proffer a resolution from the perspective of integrable Weyl geometry: The paradoxes rest on the failure to recognise a more apposite spacetime setting for NG.

中文翻译：

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揭开Nordström重力的三个奥秘

摘要本文重新审视了诺德斯特罗姆的标量引力理论（NG）–可以说是广义相对论出现之前最有说服力的相对论引力论。它以两种不同的形式存在。在诺德斯特罗姆（Nordstrom）的原始作品（1913年）中，NG似乎描述了Minkowski时空的标量引力场。在爱因斯坦和福克（Einstein and Fokker，1914）的版本中，NG似乎是一个时空理论：它重新构想了引力效应，将其作为非Minkowskian惯性结构的体现。NG的两种变体在基本原理的地位和有效性上产生了三个矛盾的结论：弱当量原理，重力能量的存在和能量守恒。考虑到NG的两个变体的等价性，这种模糊性似乎对时空现实主义者来说是矛盾的。一世'