论文标题
古典进化而没有进化
Classical Evolution Without Evolution
论文作者
论文摘要
Page和Wootters的众所周知的论点演示了如何在全球状态下“得出”子系统的常规量子动力学，这是Hamiltonian总体的特征。我展示了如何通过使用与量子相似的形式主义来在古典物理学中进行相同的论点。这并不奇怪，因为汉密尔顿 - 雅各比经典动力学的公式是由永恒动态的逻辑促进的。最终，获得无动力学的动力学的关键是能量保护的原理，它导致与不同子系统有关的时间之间的相关性。当然，关于所有其他保守量的人当然可以说同样的话，我们在其完整的一般性中展示了如何解决此问题，以实现旋转而不旋转，不翻译的翻译等等。然而，经典和量子解释确实有一个主要区别，这是希尔伯特（Hilbert）较高的混合物解释的教堂，仅在量子物理学中存在。我们讨论了这一点的一些后果。
The well known argument of Page and Wootters demonstrates how to "derive" the usual quantum dynamics of a subsystem in a global state which is an eigenstate of the total Hamiltonian. I show how the same argument can be made in classical physics, by using a formalism that closely resembles the quantum one. This is not surprising since the Hamilton-Jacobi formulation of classical dynamics is precisely motivated by the logic of timeless dynamics. Ultimately, the key to obtaining dynamics without dynamics is the principle of energy conservation which leads to correlations between times pertaining to different subsystems. The same can, of course, be said about all other conserved quantities and we show how to address this problem in its full generality so as to realise rotation without rotation, translation without translation and so on. The classical and quantum interpretations do, however, have one major difference and this is the Church of the Higher Hilbert Space interpretation of mixtures, which only exists in quantum physics. We discuss a few consequences of this point.
