In this paper by Sean Carroll (What if Time Really Exists), there's a section "Lessons from Duality" where he says that the holographic principle (and in particular, that a lower dimensional non-gravitational quantum theory can be dual to a higher dimensional theory of quantum gravity) suggests that the Wheeler-deWitt equation need not hold.
As I understand this, the issue is that the total energy in classical GR is zero, while the total energy in ordinary quantum field theory is typically non-zero.
But if there really is any valid argument that the total energy is zero in quantum gravity (presumably some people think this follows from the total energy being zero in classical gravity with no cosmological constant?) then the implication would seem to be that whatever conformal field theory lives on the boundary has to also have zero total energy. Instead, he seems to be drawing the opposite conclusion--that since the total energy can be anything in ordinary QFT, this duality suggests that it can be anything in quantum gravity. Is either of these a valid conclusion to draw?
