AI 中文总结
该研究指出奥斯特罗格拉德斯基定理不适用于引力系统，弱场近似因预设绝对时间会调用该定理，仅适用于普朗克尺度以下，而满足哈密顿约束的幽灵模式是时空构建的必要部分。
AI 中文摘要
奥斯特罗格拉德斯基定理表明，高阶导数动力系统必然会产生一个具有下方无界幽灵模式的哈密顿量。但我们认为该定理不适用于引力系统，因为编码背景独立性的哈密顿约束（要求总哈密顿量严格为零）成立。满足该约束的幽灵模式是时空构建的必要组成部分。需强调的是，弱场（引力子）近似作为预设绝对时间存在的背景依赖方案，会调用该定理，因此仅适用于普朗克尺度以下、二阶导数项占主导的领域。
英文摘要
Ostrogradsky's theorem shows that higher-derivative dynamical systems inevitably yields a Hamiltonian featuring a ghost mode that is unbounded from below. However, we argue that this theorem is inapplicable to gravitational systems, as the Hamiltonian constraint, which encodes background independence by dictating that the total Hamiltonian vanishes, holds strictly. The ghost mode obeying this constraint constitutes an indispensable component in the construction of space and time. Nevertheless, it should be underscored that the use of the weak-field (graviton) approximation, being a background-dependent scheme presupposing the existence of absolute time, invokes this theorem; consequently, it is allowed only in the domain below the Planck scale, where second derivative terms dominate.
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