[论文解读] Quasiclassical Domains in a Quantum Universe

James B. Hartle|arXiv (Cornell University)|Jan 1, 1993

Cosmology and Gravitation Theories被引用 4

一句话总结

本文通过识别准经典域——即退相干和粗粒化抑制量子干涉的区域——解释了在封闭宇宙中，经典确定性定律如何从量子力学中涌现。它表明，这些域源于宇宙的初始条件和哈密顿量，仅有极小部分初始态能重现我们日常经验中的准经典现实。

ABSTRACT

In this universe, governed fundamentally by quantum mechanical laws, characterized by indeterminism and distributed probabilities, classical deterministic laws are applicable over a wide range of time, place, and scale. We review the origin of these deterministic laws in the context of the quantum mechanics of closed systems, most generally, the universe as a whole. In this formulation of quantum mechanics, probabilities are predicted for the individual members of sets of alternative histories of the universe that decohere, i.e., for which there is negligible interference between pairs of histories in the set as measured by a decoherence functional. An expansion of the decoherence functional in the separation between histories allows the form of the phenomenological, deterministic equations of motion to be derived for suitable coarse grainings of a class of non-relativistic systems, including ones with general non-linear interactions. More coarse graining is needed to achieve classical predictability than naive arguments based on the uncertainty principle would suggest. Coarse graining is needed to effect decoherence, and coarse graining beyond that to achieve the inertia necessary to resist the noise that mechanisms of decoherence produce. Sets of histories governed largely by deterministic laws constitute the quasiclassical domain of everyday experience which is an emergent feature of the closed system’s initial condition and Hamiltonian. We analyse the question of the sensitivity of the existence of a quasiclassical domain to the particular form of the initial condition. We find that almost any initial condition will exhibit a quasiclassical domain of some sort, but only a small fraction of the total number of possible initial states could reproduce the everyday quasiclassical domain of our universe.

研究动机与目标

• 解释在封闭宇宙中，从基本量子定律如何涌现出经典决定论。
• 分析退相干和粗粒化如何导致我们日常经验中的准经典域。
• 研究准经典域的存在对宇宙初始量子态的敏感性。
• 确定产生与我们宇宙相似的准经典域的初始条件比例。

提出的方法

• 使用量子力学的一致历史诠释来定义一系列备选历史。
• 应用退相干泛函来度量历史之间的干涉，干涉可忽略表示退相干。
• 将退相干泛函在历史分离量上展开，以推导出运动的唯象方程。
• 施加粗粒化以抑制量子噪声，实现超越不确定性原理估计的类经典可预测性。
• 分析初始条件和哈密顿量在塑造准经典行为涌现中的作用。
• 使用统计推理评估不同初始态下准经典域的鲁棒性。

实验结果

研究问题

• RQ1 在封闭宇宙中，经典定律如何从量子力学中涌现？
• RQ2 需要多高的粗粒化程度才能实现超越不确定性原理估计的类经典可预测性？
• RQ3 准经典域的存在对宇宙初始量子态的具体形式有多敏感？
• RQ4 在可能的初始条件中，有多大比例能产生与我们日常经验相似的准经典域？
• RQ5 哈密顿量在塑造准经典域结构方面起什么作用？

主要发现

• 通过退相干和充分的粗粒化，准经典域从量子力学中涌现，实现类经典可预测性。
• 对于具有非线性相互作用的非相对论性系统，其唯象运动方程可从退相干泛函展开中推导得出。
• 为实现类经典惯性和抵抗退相干引起的噪声，所需的粗粒化程度高于不确定性原理所建议的水平。
• 几乎所有初始条件都会导致某种形式的准经典域，但仅有极小一部分能产生与我们宇宙日常类经典行为相符的域。
• 准经典域的存在对初始条件敏感，仅初始态的一个极小子集能重现观测到的类经典域。