量子统计的量子化能从经典宇宙边界条件的测量中推导出来吗？
Could quantum statistical regularities derive from a measure on the boundary conditions of a classical universe?
摘要：
本文在经典动力学理论的框架内讨论了定义宇宙边界条件的问题，指出为了解释演化的统计性质，理论中必须包含一个关于边界条件的测度。然后提出，量子统计的量子力学也可以从这个措施。利用基于经典力学和非相对论性量子力学形式主义的简化宇宙模型，给出了这种测度的明确定义。这种测度的特殊性在于它不适用于宇宙的初始条件，即粒子的初始位置和动量，而是适用于它们的初始位置和最终位置，从这些位置可以用最小作用量原理导出路径。这个问题的表述是至关重要的，它得到了以下观察的支持：把宇宙边界条件的确定比作实验室系统的准备是不正确的，在实验室系统中，系统的初始条件显然是确定的。一些可能的反对这一理论进行了讨论。具体来说，EPR悖论进行了讨论，它是解释表明，在一般情况下，对宇宙的边界条件的措施产生preinteractive相关性，并在存在这种相关性贝尔不等式不能再被证明是正确的。最后，它表明，如果一个扩大的动力学计划的理论，包括现象，如粒子的衰变和湮灭，最小作用量原理允许系统的不确定性演化。
英文摘要：
The problem of defining the boundary conditions for the universe is considered here in the framework of a classical dynamical theory, pointing out that a measure on boundary conditions must be included in the theory in order to explain the statistical regularities of evolution. It is then suggested that quantum statistical regularities also could derive from this measure. An explicit definition of such a measure is proposed, using both a simplified model of the universe based on classical mechanics and the non-relativistic quantum mechanics formalism. The peculiarity of such a measure is that it does not apply to the initial conditions of the universe, i.e. to the initial positions and momenta of particles, but to their initial and final positions, from which the path is derived by means of the least action principle. This formulation of the problem is crucial and it is supported by the observation that it is incorrect to liken the determination of the boundary conditions of the universe to the preparation of a laboratory system, in which the initial conditions of the system are obviously determined. Some possible objections to this theory are then discussed. Specifically, the EPR paradox is discussed, and it is explained by showing that, in general, a measure on the boundary conditions of the universe generates preinteractive correlations, and that in the presence of such correlations Bell's inequality can no longer be proven true. Finally, it is shown that if one broadens the dynamical scheme of the theory to encompass phenomena such as particle decay and annihilation, the least action principle allows for an indeterministic evolution of the system.
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