arXiv 0906.02942009-06-01quant-ph

量子测度理论的新解释

Quantum Measure Theory: A New Interpretation

Yousef Ghazi-Tabatabai

备注：: Thesis, 155 pages

摘要：

量子测度理论可以作为哥本哈根量子力学在经典随机理论中的一种基于历史的重新表述（和推广）。这些经典模型适合于一种简单的解释，即一个单一的历史（样本空间的一个单一元素）被认为是“真实的”;我们只要求这个真实的历史不应该被动力学排除在外，动力学的公理确保了不是所有的历史都被排除在外。然而，将这种解释天真地应用于量子测度理论，我们可以找到实验上可实现的系统（特别是佩雷斯-科亨-斯佩克系统），其中每一个历史都被动力学排除，这对我们提出了更深层次的实在论框架的挑战。我们的第一个反应是坚持我们现有的解释框架，并试图修改动力学，将量子测度理论还原为经典动力学。我们探讨这种方法，通过检查一个简单的（离散）零格的随机崩溃模型的历史制定，得出结论，这种方法的缺点超过了好处。我们的第二个反应是放弃我们的古典启发的解释，支持索尔金的“共同事件”，一个更一般的本体论，仍然允许严格的现实主义。在这种情况下，理论的“潜在真实”对象（贝尔语言中的“beables”）不是个体历史，而是真理评价图或共同事件。我们开发和评估各种共事件方案，已建议到目前为止，最后采用乘法方案，目前的工作模型的共事件理论和量子测量理论的一个有前途的解释，虽然仍在进行中的工作。最后，我们探索在这个新的框架中的动态和预测的表达。

英文摘要：

Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models lend themselves to a simple interpretation in which a single history (a single element of the sample space) is deemed to be 'real'; we require only that this real history should not be ruled out by the dynamics, the axioms of which ensure that not all histories are precluded. However, applying this interpretation naively to quantum measure theory we can find experimentally realisable systems (notably the Peres-Kochen-Specker system) in which every history is ruled out by the dynamics, challenging us to formulate a deeper realist framework. Our first response is to hold on to our existing interpretative framework and attempt a revision of the dynamics that would reduce quantum measure theory to a classical dynamics. We explore this approach by examining the histories formulation of a stochastic-collapse model on a simple (discrete) null-lattice, concluding that the drawbacks of this approach outweigh the benefits. Our second response is to abandon our classically inspired interpretation in favour of Sorkin's 'co-events', a more general ontology that still allows for strict realism. In this case the 'potentially real' objects of the theory (the 'beables' in Bell's language) are not individual histories but truth valuation maps, or co-events. We develop & evaluate various co-event schemes that have been suggested to date, finally adopting the multiplicative scheme; the current working model of co-event theory and a promising interpretation of quantum measure theory, though still a work in progress. We conclude by exploring the expression of the dynamics & predictions in this new framework.

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