关于引力场性质的一个超越量子理论的不可行定理
A no-go theorem on the nature of the gravitational field beyond quantum theory
摘要：
最近，人们提出了用大质量量子系统进行桌面实验来检验量子理论和引力的界面。特别是，争论的关键点是，如果两个量子系统仅仅由于引力相互作用而纠缠，是否有可能对引力场的量子性质得出任何结论。通常，这个问题已经通过假设一个特定的物理理论来描述引力相互作用来解决，但是没有系统的方法来解释与纠缠观测相兼容的可能的引力理论。在这里，我们通过引入广义概率论（GPTs）的框架来研究引力场的性质来弥补这一点。这个框架使我们能够系统地研究所有与探测两个系统之间的引力相互作用产生的纠缠相兼容的理论。我们证明了一个不可行定理，说明以下陈述是不相容的：i）引力能够产生纠缠; ii）引力介导系统之间的相互作用; iii）引力是经典的。我们分析了每个条件的违反，特别是关于替代非线性模型，如薛定谔-牛顿方程和崩溃模型。
英文摘要：
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
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