Do quantum gravity corrections to Schrodinger evolution violate unitarity?
In plain words
Ordinary time-dependent quantum mechanics can be recovered from the timeless Wheeler-DeWitt equation by treating gravity as a slow variable. The next corrections in this approximation appear to break conservation of probability, and it is unclear whether this is real or an artifact.
Precise statement
In the Born-Oppenheimer expansion of the Wheeler-DeWitt equation in powers of $1/m_P^{2}$ (Kiefer and Singh 1991), the matter wave function obeys a Schrodinger equation with time defined by the gravitational WKB phase, plus $O(1/m_P^{2})$ correction terms that are not Hermitian with respect to the naive inner product. Determine whether an inner product and choice of clock exist that make the corrected evolution unitary order by order. An answer is a construction or a proof that the $O(1/m_P^{2})$ unitarity violation is physical.
What would settle it
An order-by-order construction of a conserved inner product for the Born-Oppenheimer expansion, or a proof that none exists.
Status in the literature
Unverified note
Competing constructions of unitary corrected evolution have been proposed (for example Kiefer and Wichmann 2018) without consensus as of 2026.