New essay asking “Is Holography Implicit in Canonical Gravity?” The precise conjecture is that if two solutions of the Wheeler-deWitt equation coincide near the boundary of anti-de Sitter space at one point of time, then they must be equal. (i.e. they cannot differ even in the bulk.)
https://arxiv.org/abs/1903.11073
Of course, such a claim cannot hold in the classical theory—where it is easy to construct metrics and matter configurations that differ in the bulk but coincide asymptotically—but the essay lays out some evidence that the quantum theory does have this property.
This property might not sound surprising to string theorists but in talking to people who work in canonical gravity, I often get the impression that they think of holography as something mysterious that emerges from the ultraviolet properties of string theory. The suggestion here is that this is not the case, and holography is implicit even in the low-energy canonical formulation of quantum gravity.
If you have comments, please send them to me, especially if you find the argument provocative/wrong/obviously right!
(This post comes with the usual apologies to my non-physics friends if Facebook puts this on your timeline.)