We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schrdinger wave-function under arbitrary frame changes.

中文翻译：

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非相对论几何和等效原理

我们描述了非相对论物理学中等效原理的基于几何和对称的公式。它适用于经典和量子水平，并指出可以消除牛顿势，以支持弯曲和时间相关的空间度量。正是这个要求迫使重力质量等于惯性质量。我们将负责等效原理的对称性确定为相对论的时间重新参数化对称性的残余。我们还阐明了薛定谔波函数在任意坐标系变化下的变换性质。