论文标题
自由落下KVN力学和爱因斯坦的等价原则
Free fall in KvN mechanics and Einstein's principle of equivalence
论文作者
论文摘要
讨论了爱因斯坦在Koopman-von Neumann（KVN）力学中的等价原则的实施。实施与在量子力学中实施该原理非常相似。这并不奇怪，因为KVN力学提供了与量子力学形式主义非常相似的经典力学的希尔伯特空间公式。 在KVN力学和量子力学中，均匀的引力场中的传播器都与自由传播器相关。结果，在自由下降的参考帧中均质重力场中的波函数与自由波函数仅在相位上有所不同。 Fisher信息量化了我们从坐标测量值估算质量的能力，并不取决于同质重力场的大小，并且这一事实构成了爱因斯坦等效原理的制定，这在量子力学和KVN机制中都是有效的。
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.
