  Runaway solutions can be avoided in fourth order gravity by a doubling of the
matter operator algebra with a symmetry constraint with respect to the exchange
of observable and hidden degrees of freedom together with the change in sign of
the ghost and the dilaton fields. The theory is classically equivalent to
Einstein gravity, while its non-unitary Newtonian limit is compatible with the
wavelike properties of microscopic particles and the classical behavior of
macroscopic bodies, as well as with a trans-Planckian regularization of
collapse singularities. A unified reading of ordinary and black hole entropy
emerges as entanglement entropy with hidden degrees of freedom.
