I would like to mention a precursor to some tensor network-entanglement stuff I see being bandied about. Since the mid-nineties we developed in many papers what we called the Structurally Dynamic Cellular Network Approach to Quantum Space-Time Physics. A recent review is arXiv: 1501.00391. In arXiv:gr-qc/0110077 (J.Math.Phys. 44(2003)5588) they constructed a Geometric Renormalization Group dealing with the various hierarchies of entanglement up to continuous space-time. In arXiv: 0910.4017 they introduced so-called Wormhole Spaces as the common cause of BH Entropy-Area Law, the Holographic Principle and Quantum Entanglement.
If one is tempted to attribute "universality" to the connection between entanglement and gravity one will end up with nothing... for clarity, do we know if one referring to the same universality first coined by Leo Kadanoff)? If so, it seems we're well on the eponymous way to covering the ToE bases from the quantum to the relativistic, via the classical scale - including consciousness itself, just as Roger Penrose predicted over 20 years ago.
This is not the first SF novel exploring tensor networks and quanta gravity in tandem. There is a whole programme going on employing tensor network renormalization group techniques to understand better the continuum limit of spinfoam models for quantum gravity:
http://arxiv.org/abs/1109.4927
http://arxiv.org/abs/1306.2987
http://arxiv.org/abs/1311.1798
http://arxiv.org/abs/1311.7565
http://arxiv.org/abs/1312.0905
http://arxiv.org/abs/1409.2407
Some "smart cookies" have become totally lost in a metaphysical swampland (quantum weirdness) of their own creation, in spite of being repeatedly warned about this prospect. Rather than running away from (attempting to actually explain) all the supposed weirdness, they have been gleefully running towards it for decades. Now, they have ventured so far "over the horizon" that separates physics from metaphysical speculation, that they could not see Newton's head, as he stands on the shoulders of giants, even if they tried. They have lost all sight of reality (Newton pretended objects having mass were dimensionless points and time had no effect.)
“Schild’s Ladder” is about a theory, i.e. a *model*, i.e., a useful lens through which to view something, because it provides a reasonably detailed story of how one thing leads to another. Models (epistemology) are not Reality (entomology). I think most people need to be reminded of that frequently. Speculation & intuition are valid strategies, but they're vague or incomplete approximations, hints, and clues, useful for building a model. But they're not models attempting to explain a particular *aspect* of Reality, much less Reality Itself (whatever that is). Reading that AdS space has negative vacuum energy and shrinks away to nothing, and our universe has positive vacuum energy and expands without bound makes me wonder if anyone has considered the possibility that AdS space and our universe exist in some kind of time-energy symmetry. I'm sure something this simple (well, this simple to cosmologists) has been considered, but I've never seen anything written about it.
What if in the holographic duality gravity (as graviton particles) was switched to the boundary and quantum particles were placed in the higher dimensional bulk as gauge fields which would be kind of an inverse situation. Could this translate to a de Sitter space? Also, could Michael Freedman's E8 manifold which generates a non-smooth 4 dimensional manifold be quantum error corrected to a smooth 4D-manifold? This is the good stuff Egan uses to build up and support his SFional universe and what a ride it was!
Egan’s stuff explores ideas. Examinations of a universe. The fact that the characters are unrealistic is totally missing the point. I also enjoy the later work, but they can require more concentration, though they can be very rewarding for that. “Schild’s Ladder” in particular really bent my brain despite having a minor in physics. But still, it's a great book! For a person new to Greg Egan reading them in rough order would probably be no bad thing (which is what I’ve been doing since the beginning of 2019, because I came to the conclusion that I had only written one review of an Egan’s novel: “Permutation City”). “Schild's Ladder” was one of the hardest hard SF I've ever read (you can read it for the plot, but the plot is only half the fun).
NB: The review above was written many years ago. I just changed it to 2019 to incorporate some new stuff. Over the years, after I published the review above, the question I always got was: “Why Schild's Ladder as the title of the book?” and I always answered “Ah! There's the rub. If you didn't get that the book is not for you.” In 2019 I finally re-read it and here’s the “explanation”. What do a parallel transport of vectors on a manifold got to do with the novel? The concept of "tangent vectors" in a manifold also involves a "tangent bundle" which is a sort of "tangent space" at each point on that manifold. Alfred Schild "invented" a way of doing parallel transport of those vectors. Imagine you want to do a parallel transport of a vector around a closed loop on a sphere like the ship’s spin in the novel: “To his left, the ship’s spin was clearly visible against the backdrop of stars, all the more so because the axis of rotation coincided with the direction of travel.” The angle by which it twists is always proportional to the area inside the loop: this means that if you start drawing tangents to all points maintaining the same direction at all times, the tangent will arrive at the starting point at a certain angle (when you compare the starting vector and the final vector). This is hard to explain without a visual aid. Suffice to say, the geometrical path on the “nova-vacuum” sphere (it can be extended to a manifold which is a more general Space) looks like a ladder!!!! Egan, in a way, questions the old philosophical theme whether we are the same person at the beginning and at the end...Are we the same “tangent” as before? Are we another “tangent”? Not only is this notion used to explain (by analogy) how we can tell, from time to time, whether we are the same person, but the manifold fact that sometimes parallel transport of the same starting tangent around different paths (on a manifold) with the same endpoints will always produce different resulting tangents! As the omniscient narrator states: “All an organism could do from day to day was shore itself up in some rough semblance of its previous condition. The same was true, from moment to moment, for the state of the while universe. By one means or another, everyone was an imperfect imitation of whatever they’d been the day before.” I gave this novel 5 stars back in the day. In 2019 I’d give it 6 stars if I could…
