In this essay based on 0907.2939, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. Disentangling the degrees of freedom associated with two regions of spacetime results in these regions pulling apart and pinching off from each other in a way that can be quantified by standard measures of entanglement.
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My "cognitive white noise generator" has been locked on emergent spacetime for a decade now. The idea here, and I'm very loosely summarizing, is that the dimensions themselves are emergent properties of large scale entanglement - the mathematical "dimensions" resolve quite well into flesh and blood, "this is a chair" dimensions.
The paper that sort of kicked it off
https://arxiv.org/abs/1005.3035
Quite evocative, but would require spectacularly sensitive testing apparatus to falsify . . and even then, other explanations aplenty.
It is the fabric of space, after all, no shortage of theories.
One of the most important papers in this field is [0]. (As is common in science, it built on a long history of nearby ideas, e.g. [1].) An important calculation done around this idea is presented in [2], in which remarkable progress is made on Hawking's black hole information paradox. All of these papers have some amount of mathematical backing, but you'll find plenty of formulas and calculations in [2]!
[0] https://arxiv.org/abs/1306.0533
[1] https://arxiv.org/abs/1005.3035
[2] https://arxiv.org/abs/1908.10996
I think SW became too obsessed with the mathematical and computational approach to CA, while (as usual) 't Hooft pursued his physics intuitions to create a candidate CA theory:
https://arxiv.org/abs/1405.1548
I say as usual, because G'tH had already formulated the holographic principles that would allow space-time (hence GTR) to be encoded non-locally over a graph.
https://arxiv.org/abs/gr-qc/9310026
There need not be a preferred reference frame if the space-time events do not occur at individual nodes in the graph, but emerge at scales much larger than the graph, with some holographic or permutation symmetry that can reproduce the diffeomorphism invariance of GTR. It is…
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also plausible that the position-momentum duality of space-time could emerge from such a theory.
Space-time would be created by the events that occur, not the other way around, hence the aphorism spooky distance at an action, because the events are primary, and distance is the strange phenomenon that emerges from them.
There has been much recent progress in making space emerge from entanglement, which also implies that locality emerges from non-locality:
https://arxiv.org/abs/1005.3035
https://phys.org/news/2015-05-spacetime-built-quantum-entang...
https://www.scientificamerican.com/article/tangled-up-in-spa...
Note that LQG has produced a nice discretization of space, based on graphs that have observable quanta of area and volume, but not length. Directions and lengths are defined as normals to areas, which is reminiscent of Clifford Algebra. Having derived (emergent) lengths also makes diffeomorphism easier.
https://arxiv.org/abs/gr-qc/9411005
The links to the original papers:
older one: http://arxiv.org/abs/1005.3035v1
recent one: http://arxiv.org/abs/1306.0533
Very cool. The paper suggests a connection between the non-local properties of EPR pairs and the non-local properties of wormholes that connect distant regions of space time.
EPR pair = Einstein-Podolsky-Rosen pair, e.g.
|Phi〉 = |0〉⊗|0〉+ |1〉⊗ |1〉. (1)
The vectors to the left of ⊗ represent the state of Alice, the vectors to the right of the ⊗ represent Bob's state. The + in the equation refers to the notion of quantum superposition.
There is nothing mysterious about quantum superposition. You know how y=sin(x) and y=cos(x) are both solutions to…
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y''+y=0? Well then any linear combination of sin and cos is also a solution:
y = a*sin(x) + b*cos(x).
Similarly, in QM, a quantum states |v〉is described by linear combinations of some reference vectors |0〉and |1〉
|v〉 = a|0〉+ b|1〉.
For example, the vector |+〉=|0〉+ |1〉 points half-way between the direction |0〉and |1〉.
However, we cannot describe |Phi〉as the tensor product of two local descriptions:
|0〉⊗|0〉+ |1〉⊗ |1〉 ≠ (a|0〉+ b|1〉) ⊗ (c|0〉+ d|1〉) for any a,b,c,d \in C.
Because |Phi〉, the quantum state of an EPR pair cannot be written in terms of local descriptions. We say EPR pairs are non-local. The equation of the state |Phi〉(see equation (1) above) is a description of the combined state of Alice and Bob.
Their states are entangled. If upon measuring Alice's state we find it to be |0>, then we know immediately that Bob's state is also |0>. Because of the entanglement, the collapse in the superposition on Alice's side immediately causes a collapse of the superposition on Bob's side. Note that Bob's collapse will occur IMMEDIATELY, and no matter how far Bob's system is from Alice's. This is what the authors Einstein, Podolsky and Rosen called "spooky action at a distance."
Now imagine you have have a whole bunch of physical systems prepared so their state is an EPR pair. Alice has the left halfs of the EPR pairs, Bob has all the right halfs. Now Alice's systems collapse into a black hole and Bob's systems collapse into their own black hole. The connection that will exist between these black holes appears to be similar to the wormholes connecting black holes ("Einstein-Rosen bridge"s), which have been studied in general relativity.
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will.