Einstein’s Equivalence Principle implies that the Lorentz force equation can be derived from a geodesic equation by imposing a certain (necessary) condition on the electromagnetic potential (Trzetrzelewski, EPL 120:4, 2018). We analyze the quantization of that constraint and find the corresponding differential equations for the phase of the wave function. We investigate these equations in the case of Coulomb potential and show that physically acceptable solutions do not exist. This result signals an inconsistency between Einstein’s Equivalence Principle and Relativistic Quantum Mechanics at an atomic level.

中文翻译：

---

等价原理与相对论量子力学

爱因斯坦的等效原理意味着洛伦兹力方程可以通过对电磁势强加特定（必要）条件从测地方程导出（Trzetrzelewski，EPL 120：4，2018）。我们分析该约束的量化并找到波函数相位的相应微分方程。我们在库仑势的情况下研究这些方程，并表明不存在物理上可接受的解决方案。这一结果表明爱因斯坦的等效原理和相对论量子力学在原子水平上存在不一致。