The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism. Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase. Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.

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KvN 力学中的自由落体和爱因斯坦的等效原理

讨论了爱因斯坦等效原理在 Koopman-von Neumann (KvN) 力学中的实现。该实现与量子力学中该原理的实现非常相似。这并不奇怪，因为 KvN 力学提供了经典力学的希尔伯特空间公式，它与量子力学形式主义非常相似。在 KvN 力学和量子力学中，均质引力场中的传播子与自由传播子简单相关。因此，自由落体参考系中均匀引力场中的波函数与自由波函数仅在相位上不同。Fisher 信息量化了我们从坐标测量中估计质量的能力，不依赖于均匀引力场的大小，