Dear Janko
thank you for your interesting post. Yes, my approach is close to that of Fotini, in the sense that we reach the same conclusion, namely that, as she says:
"the problem of time is a paradox, stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is not time but space, geometry and gravity. The quantum theory of gravity will be spaceless, not timeless. If we are willing to throw out space, we can keep time and the trade is worth it. "
The supporting technical material you are asking is given in the following Refs. in my essay:
[7] G.M. D'Ariano and P. Perinotti, arXiv preprint 1306.1934 (2013) http://arxiv.org/abs/1306.1934
[8] M. Kapovich, Cayley graphs of finitely generated in- finite groups quasi-isometrically embeddable in R3, http://mathoverflow.net/questions/130994 version: 2013-05-17
To say something more Alice and Bob and how space emerges from systems, the logic is the following. You start from relations between systems. If you assume that they are homogeneous, then they are described by a finitely-generated infinite group. From that group you get the manifold that embeds it quasi-isometrically. Therefore the manifold emerges from relations. The striking thing is that the quantum cellular automaton achieves the embedding "physically", in the sense that all the continuous symmetries are recovered from the discrete in the limit of small wave-vectors (the relativistic limit). It is the quantum nature of the related systems that allows this, and this is exactly the idea that I wrote in my previous essay in an embryonic stage, namely that the quantum superposition of paths solves the Weyl-tiling issue of recovering continuum geometry from the discrete one. Therefore, the quantum nature of systems and relations is crucial for the emergence. This new way of having space-time as emergent from a purely relational framework is amazingly interesting, since it also opens crucial new problems (e.g. if there are QCA that are quasi-isometrically embeddable in non euclidean spaces!). I'm now in Chicago where I will meet some mathematicians expert in the field, and I hope to find answers soon.
As regards consciousness, I never seriously addressed this problem. I saw your essay, and it looks interesting, but I need time to read it. I will doit, hopefully in time to rate the essay.
My best regards
Mauro