The Ostrogradsky instability can be overcome by quantum physics: https://arxiv.org/abs/2105.00898
John F Donoghue, Gabriel Menezes
In theories with higher time derivatives, the Hamiltonian analysis of Ostrogradsky predicts an instability. However, this Hamiltonian treatment does not correspond the way that these theories are treated in quantum field theory, and the instability may be avoided in at least some cases. We present a very simple model which illustrates these features.
Comments: 11 pages, 2 figures