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PreprintCC BY 4.0arXiv

Ostrogradsky's Theorem is Incompatible with Background Independence in Quantum Gravity

  • Ken-ji Hamada
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Abstract

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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Cite

BibTeXRIS
BibTeX
@misc{hamada2026ostrogradskys,
  title = {{Ostrogradsky's Theorem is Incompatible with Background Independence in Quantum Gravity}},
  author = {Ken-ji Hamada},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.17364},
  eprint = {2608.17364},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.17364},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ostrogradsky's Theorem is Incompatible with Background Independence in Quantum Gravity
AU  - Ken-ji Hamada
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.17364
UR  - https://arxiv.org/abs/2608.17364
AB  - 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.
ER  -