[论文解读] Causal Wave Mechanics and the Advent of Complexity. IV. Dynamical origin of quantum indeterminacy and wave reduction

Andrei P. Kirilyuk|ArXiv.org|Nov 23, 1995

Quantum Mechanics and Applications参考文献 10被引用 9

一句话总结

本文通过将测量过程建模为量子物体与耗散仪器构成的复合系统中的不稳定性，提出了一种动态的、因果的量子不确定性和波函数坍缩的解释。波函数由于多值有效动力学而动态地‘收缩’至局域化实现，量子概率由此类根本性动力学不确定性导出，无需引入经典或随机假设。

ABSTRACT

The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the quantum measurement process. The modified Schroedinger formalism involving multivalued effective dynamical functions reveals the dynamic origin of quantum measurement indeterminacy as the intrinsic instability in the compound system of 'measured object' and (dissipative) 'instrument' with respect to splitting into spatially localised 'realisations'. As a result, the originally wide measured wave catastrophically (and really!) "shrinks" around a random accessible point thus losing all its 'nonlocal properties' with respect to other points/realisations. The dissipativity of one of the interacting objects (serving as 'instrument') is reduced to its (arbitrarily small) openness towards other systems (levels of complexity) and determines the difference between quantum measurement and quantum chaos, the latter corresponding to an effectively isolated system of interacting (micro-) objects. We do not use any assumptions on particular "classical", "macroscopic", "stochastic", etc. nature of the instrument or environment: physical reduction and indeterminacy dynamically appear already in interaction between two microscopic (quantum) deterministic systems, the object and the instrument, possessing just a few degrees of freedom a part of which, belonging to the instrument, should correspond to locally starting, arbitrarily weak excitation. This dynamically indeterminate wave reduction occurs in agreement with the postulates of the conventional quantum mechanics, including the rule of probabilities, which transforms them into consequences of the dynamic uncertainty.

研究动机与目标

• 为量子测量的非定域性与波函数坍缩提供一种因果的、确定性的解释。
• 通过展示波函数塌缩源于物体与仪器构成的复合系统中的内在不稳定性，解决测量问题。
• 确立量子概率源于根本性动力学不确定性，而非作为公设提出。
• 通过引入耗散性作为关键因素，区分量子测量与量子混沌。
• 消除对测量装置的古典、宏观或随机假设的依赖。

提出的方法

• 引入多值有效动力函数，以建模‘被测物体’与‘仪器’构成的复合系统。
• 应用改进的薛定谔形式体系，描述在动力学不确定性下的系统演化。
• 将仪器建模为对其他系统具有耗散性开放的系统，即使耦合强度极小亦成立。
• 分析波函数在分裂为局域化‘实现’时的不稳定性。
• 证明波函数坍缩是由于该不稳定性导致的灾难性、真实的物理过程。
• 表明局域化结果的概率与玻恩定律一致，该定律由此类动力学不确定性导出。

实验结果

研究问题

• RQ1 量子非定域性是否可由物体-仪器系统中的动力学不稳定性来解释？
• RQ2 波函数坍缩如何在无外部公设的前提下，由确定性、因果的动力学产生？
• RQ3 在系统开放性与耗散性方面，量子测量与量子混沌有何区别？
• RQ4 量子测量的概率性质能否从根本性动力学不确定性中导出？
• RQ5 即使在自由度较少的系统中，坍缩过程是否仍为真正物理且不可逆？

主要发现

• 量子非定域性源于物体与仪器复合系统的内在不稳定性，而非公设的随机性。
• 波函数坍缩是由于多值动力学不确定性导致的真实、灾难性收缩，最终局域化为某一实现。
• 该过程完全因果且确定，无需依赖经典或宏观测量装置。
• 局域化结果的概率与玻恩定律一致，玻恩定律由此类动力学不确定性成为自然结果。
• 仪器的耗散性——定义为对其他复杂层次的最小开放性——是区分测量与量子混沌的关键。
• 该理论适用于自由度较少的微观系统，表明波函数塌缩并非本质上依赖宏观尺度。