Voevodskiĭ’s Conjecture
Tonight I had a dream that in 1998 there was a conference in Montréal, or in some nature’s resort in Canada, where Volodya Voevodskiĭ proposed that the remaining part of the knowledge (in the black hole information paradox) is contained in “the bulk” of observed universe of a (post-)quantum observer, and can be algebraised (using some version of homotopy type theory) into additional dimensions, tensored out as corresponding to another equally valid observer. Even Jurek Lewandowski was inspired by this possible “information theoretic algebraisation” of the problem of the observer. This was somehow connected with the bounds on information transmission provided by Cirel’son numbers (as if the availability of “higher order” tensorial structures could provide useful local invariants to quantify the homotopical structure of how the knowledge of two observers is recombined into a single universe). There was also some proof (called the “Infinity Conjecture”) that “Voevodskiĭ’s dimensional composition” does not hold if a certain condition is not satisfied (I don’t remember that condition). There was a feeling of a profound parallelity of cutting-edge developments between ∞-categorical homotopy type theory on one side and space-time emergence from local post-quantum information theory of relational observers on the other side (the latter driven by two communities: quantum information foundations and post-string theory “information theoretic” QFT).
What if: an intrinsic geometry and dynamics of one observer is “ignorance–glued” into a “bulk” (external/“dissipative”) geometry and dynamics of the other?
10.XII.15, Waterloo