[论文解读] Contingent Free Choice: On Extending Quantum Theory to a Contextual, Deterministic Theory With Improved Predictive Power

Ghislain Fourny|arXiv (Cornell University)|Jul 3, 2019

Quantum Mechanics and Applications参考文献 21被引用 1

一句话总结

本文通过用有条件的自由选择替代独立自由选择的假设，提出了一种上下文相关的、确定性的量子理论扩展，借助博弈论推理提升了预测能力。通过将量子测量建模为具有不完美信息的动态博弈，作者在完美预测下通过迭代剔除不一致的世界，推导出唯一确定的结果，从而在不违反贝尔不等式的情况下解决了EPR类悖论。

ABSTRACT

The non-extensibility of quantum theory into a theory with improved predictive power is based on a strong assumption of independent free choice, in which the physicists pick a measurement axis independently of anything that couldn't have been caused by their decision. Independent free choice is also at the core of the Nash equilibrium and classical game theory. A more recent line of game-theoretical research based on weakening free choice leads to non-trivial solution concepts with desirable properties such as at-most uniqueness, Pareto optimality, and contextuality. We show how introducing contingent free choice in the foundations of quantum theory yields a class of deterministic and contextual theories with an improved predictive power, and contrast them with the pilot-wave theory. Specifically, we suggest that quantum experiments, such as the EPR experiment, involving measurements located in spacetime, can be recast as dynamic games with imperfect information involving human agents and the universe. The underlying idea is that a physicist picking a measurement axis and the universe picking a measurement outcome are two faces of the same physical contingency phenomenon. The classical, Nashian resolution of these games based on independent free choice is analogous to local hidden variable theories, constrained by the Bell inequalities. On the other hand, in a setup in which agents are rational and omniscient in all possible worlds, under contingent free choice, the Perfectly Transparent Equilibrium provides a contextual resolution, based on the iterated elimination of inconsistent worlds, towards an at-most unique possible world, in which the outcomes of measurements that actually are carried out, and only them, are deterministically defined.

研究动机与目标

• 挑战量子理论中独立自由选择这一基础假设。
• 通过弱化自由选择假设，发展一种具有增强预测能力的确定性、上下文理论。
• 利用博弈论框架解决量子测量悖论（如EPR实验中的悖论）。
• 表明条件自由选择可通过完美预测和理性一致性，导致唯一确定的结果。
• 与德布罗意-玻姆理论和局部隐变量模型进行对比，强调其更优的预测结构。

提出的方法

• 将量子测量建模为涉及物理学家和宇宙作为理性代理人的、具有不完美信息的动态博弈。
• 应用博弈论中的完全透明均衡（PTE）概念，其中代理人在所有可能世界中均理性且全知。
• 通过迭代剔除不一致的世界，识别出唯一至多一个与完美预测一致的可能世界。
• 将物理定律（如量子势、费马原理）解释为宇宙的效用最大化行为。
• 将EPR实验重新解释为一个博弈，其中测量选择与结果由理性代理共同决定。
• 在量子上下文性和条件自由选择下的理性决策之间建立正式联系。

实验结果

研究问题

• RQ1 能否通过弱化独立自由选择假设，将量子理论扩展为具有增强预测能力的确定性、上下文理论？
• RQ2 条件自由选择（即选择依赖于预测结果）如何改变量子测量结果的结构？
• RQ3 何种博弈论解概念可在保持确定性和上下文性的同时解决量子测量悖论？
• RQ4 在量子实验背景下，完全透明均衡与纳什均衡有何不同？
• RQ5 能否将宇宙建模为一个最大化预测效用的理性代理，从而导致唯一确定的结果？

主要发现

• 本文通过在条件自由选择下将完全透明均衡应用于EPR类实验，推导出量子测量的唯一确定结果。
• 所提出的理论通过拒绝独立自由选择的假设（该假设是局部隐变量模型的基础），避免了贝尔不等式的违反。
• 通过迭代剔除不一致的世界的方法，得出唯一至多一个与双方（代理人和宇宙）完美预测一致的可能世界。
• 该方法提供了一种上下文性、确定性的替代方案，以取代德布罗意-玻姆理论，仅对实际执行的测量定义结果。
• 该框架通过将测量选择与结果建模为理性的、相互依赖的决策，调和了确定性与量子上下文性。
• 该理论表明，量子随机性可能并非根本性的，而是源于假设独立自由选择，而本文认为该假设在物理上是站不住脚的。