[论文解读] Quasiclassical Realms in a Quantum Universe

James B. Hartle|ArXiv.org|Apr 11, 1994

Cosmology and Gravitation Theories参考文献 1被引用 3

一句话总结

本文提出，在一个封闭的量子宇宙中，通过退相干和粗粒化，经典确定性定律可从量子力学中涌现。研究表明，准经典领域——与日常经验一致——源于宇宙的初始条件和哈密顿量，仅有极小部分初始态能再现我们特定的经典现实。

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 laws in the context of the quantum mechanics of closed systems, most generally, the universe as a whole. There probabilities are predicted for members of decoherent sets of alternative histories of the universe, ie ones for which the interference between pairs in the set is negligible as measured by a decoherence functional. An expansion of the decoherence functional in the separation between histories allows the form of the 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 for decoherence, and coarse graining beyond that for the inertia necessary to resist the noise that mechanisms of decoherence produce. Sets of histories governed largely by deterministic laws constitute the quasiclassical realm of everyday experience which is an emergent feature of the closed system's initial condition and Hamiltonian. We analyse the sensitivity of the existence of a quasiclassical realm to the particular form of the initial condition. We find that almost any initial condition will exhibit a quasiclassical realm of some sort, but only a small fraction of the total number of possible initial states could reproduce the everyday quasiclassical realm of our universe. (Talk given at the Lanczos Centenary Conference, North Carolina State University, December 15, 1993.)

研究动机与目标

• 解释在封闭量子系统中，经典确定性定律如何从本质上是量子力学的定律中涌现。
• 研究退相干和粗粒化在准经典领域形成中的作用。
• 分析准经典领域存在性对宇宙初始量子态的敏感性。
• 阐明为何经典可预测性所需的粗粒化程度，超过不确定性原理所暗示的程度。
• 确定在何种条件下，宇宙的初始态会导向一个类似于我们日常经验的准经典领域。

提出的方法

• 使用一致历史框架，为封闭量子系统中的不同历史序列定义概率。
• 对历史之间分离的退相干泛函进行微扰展开，推导出确定性运动方程。
• 引入粗粒化以抑制量子干涉，实现退相干。
• 证明额外的粗粒化是必要的，以抑制退相干机制带来的量子噪声，从而稳定动力学行为。
• 分析准经典领域形成对初始量子态形式的依赖性。
• 采用具有普遍非线性相互作用的非相对论性模型，说明经典行为的涌现。

实验结果

研究问题

• RQ1 确定性经典定律如何从本质上是概率性和非确定性的量子力学定律中涌现？
• RQ2 粗粒化在实现退相干和经典可预测性中起什么作用？
• RQ3 为何经典行为所需的粗粒化程度，超过不确定性原理所暗示的程度？
• RQ4 准经典领域的存在对宇宙初始量子态的具体形式有多敏感？
• RQ5 有多少比例的可能初始条件会导致一个类似于我们观测到的宇宙的准经典领域？

主要发现

• 准经典领域源于宇宙的初始条件和哈密顿量，而非基本定律。
• 仅靠退相干不足以实现经典可预测性；必须通过额外的粗粒化来抑制退相干机制带来的噪声。
• 几乎所有初始条件都会导致某种形式的准经典领域，但仅有极少数能再现我们宇宙中特定的准经典领域。
• 对于合适的粗粒化，确定性运动方程可从退相干泛函的微扰展开中推导得出。
• 经典行为的涌现取决于初始量子态的结构，仅有极小一部分初始态能产生我们熟悉的经典世界。
• 该框架支持经典性是封闭系统中量子力学的涌现特性，而非基本属性的观点。