We present an exact quantum observable analog of the weak equivalence principle for a ‘relativistic’ quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as p _µ , rather than p ^µ . We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

中文翻译：

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海森堡图中量子力学的等效原理

我们提出了“相对论”量子粒子弱等效原理的精确量子可观测模拟。量子测地线方程是从海森堡运动方程获得的，作为完全协变经典哈密顿演化图的精确模拟，正确识别规范动量变量为p _µ ， 而不是p ^µ 。我们讨论与射影测量相关的方程的含义，以及具有解曲线的方程（如时空非交换几何图中的方程），以及量子引力的一种合理方法，作为一种关于量子可观测量作为物理量的理论，包括量子的概念坐标变换。