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arXiv 0812.0238quant-ph
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宏观实在论的量子破坏与向classical physics的转变

Quantum violation of macroscopic realism and the transition to classical physics

Johannes Kofler

摘要:

量子领域和宏观经典世界的描述不仅在数学表述上,而且在基本概念和哲学后果上都有很大的不同。物理系统何时以及如何停止量子力学行为并开始经典行为,在物理学界仍然存在激烈的争论,并受到理论和实验研究的影响。本文提出了一种完全在量子理论范围内的量子-经典跃迁的方法,它与现有的模型在概念上有所不同:它既不需要涉及系统的不可控环境(退相干),也不需要改变量子定律本身(坍缩模型),而是强调由于我们的测量设备的不精确性而导致的量子现象的可观测性的限制。对于某一类时间演化来说,仅仅是这种对粗粒度测量的限制,就足以看到宏观实在论的自然出现,甚至经典牛顿定律从完整的量子形式主义中出现。但也存在“非经典”哈密顿量,即使在模糊测量或退相干下,经典时空描述系统的时间演化仍然是不可能的。有人认为,这样的哈密顿是不可能自发实现的性质,因为他们的高度复杂性。最后一部分讨论了量子随机性的起源问题,并提出了与数学不可判定性的联系。

英文摘要:

The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.

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