Whether gravity is quantized remains an open question. To shed light on this problem, various Gedanken experiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally with another distant system, where an apparent paradox arises: even for spacelike separation the outcome of the interference experiment depends on actions on the distant system, leading to a violation of either complementarity or no-signaling. A recent resolution shows that the paradox is avoided when quantizing gravitational radiation and including quantum fluctuations of the gravitational field. Here we show that the paradox in question can also be resolved without considering gravitational radiation, relying only on the Planck length as a limit on spatial resolution. Therefore, in contrast to conclusions previously drawn, we find that the necessity for a quantum field theory of gravity does not follow from so far considered Gedanken experiments of this type. In addition, we point out that in the common realization of the setup the effects are governed by the mass octopole rather than the quadrupole. Our results highlight that no Gedanken experiment to date compels a quantum field theory of gravity, in contrast to the electromagnetic case.

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Gedanken 实验会强迫引力量子化吗？

重力是否被量子化仍然是一个悬而未决的问题。为了阐明这个问题，已经提出了各种 Gedanken 实验。一个流行的例子是一个大质量系统的干涉实验，该系统与另一个遥远的系统在引力上相互作用，其中出现了一个明显的悖论：即使对于类空间分离，干涉实验的结果也取决于对遥远系统的作用，导致违反任一互补性或无信号。最近的一项决议表明，在量化引力辐射并包括引力场的量子涨落时，可以避免悖论。在这里，我们表明，在不考虑引力辐射的情况下，也可以解决所讨论的悖论，仅依靠普朗克长度作为空间分辨率的限制。所以，与之前得出的结论相反，我们发现引力量子场论的必要性并不来自迄今为止考虑过的这种类型的 Gedanken 实验。此外，我们指出，在设置的常见实现中，效果由质量八极杆而非四极杆控制。我们的研究结果强调，与电磁情况相比，迄今为止，没有任何 Gedanken 实验强制使用量子引力场理论。