journal club on aspects of information, quantum theory, and gravity
30 Aug 2021
By means of a series of toy models constructed within Classical Mechanics, we shall review what is the so-called Ostrogradsky ghost in higher-order theories, i.e., theories whose Lagrangian involves higher-order time derivatives of dynamical variables. After some motivation for the consideration of such theories is provided, we shall follow (Ganz & Noui 2021) to figure out what ghosts are, which theories they haunt, and when and why one should be scared of them. In particular, we will walk through the derivation of Ostrogradsky’s Instability Theorem, see how it leads to an unbounded Hamiltonian and how it could be fixed by coupling the problematic dynamical variable to a variable without higher derivatives. This then allows one to use higher-order theories without the appearance of spooky ghosts. Still following (Ganz & Noui 2021), we then consider how the ghosts might or not manifest in quantum and/or covariant theories. At last, if time allows it, we shall briefly take a look at (Hawking & Hertog 2002) to analyze what consequences higher-derivatives might have in a quantum theory of gravity.