I've been reading Zakopane lectures on loop gravity lately and I only understood a very small part of it, but from the little I understood, I'm wondering if loop quantum gravity isn't close to describing the universe as some kind of cellular automaton.

The paper talks about space-time being considered as composed of grains connected by a graph. The way I understand it, the grains have a minimal size and can grow by steps (similar to the energy level of an electron in an atom). The size could be considered as a property of the cell (that would have many others).

A cell can impact the ones next to him and the effect of the 'content' of a cell can therefore propagate around it.

Of course, the automaton would have to be 'quantic' in the sense that its properties could be a superposition of states.

I don't have (yet ?) the understanding of the concepts of LQG to determine whether or not this would be a silly way to formulate the theory or not. Searching for it on Google, I found a few pages mentionning both terms in bold above but always as two distinct models (or even in different articles of a same site).

Has there been some studies on formulating loop quantum gravity as a cellular automaton ? Would it even make sense ?

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  • $\begingroup$ CA aren't traditionally thought to interact with cells that aren't adjacent, but that doesn't mean it can't be done, though not sure if you could get anything remotely similar to a real world model for the complexity involved. $\endgroup$ – Neil Mar 4 '16 at 12:56
  • $\begingroup$ @Neil: page 14 of the lectures, he talks about locality of the transition amplitude that I understood (maybe wrongly) as the possibility to consider only neighbours and as something compatible with cellular automaton transitions. But again, I don't understand much this part yet ... so I may have been completely misleaded by the similar term 'transition' and my previous idea that the foam was looking like a CA :-) $\endgroup$ – Colin Pitrat Mar 4 '16 at 13:08
  • $\begingroup$ I'm seeing the issue from the perspective of a physics enthusiast and professional programmer, so I couldn't tell you honestly. If the cells directly interact with many neighbors and not just say 8 surrounding cells, calculation begins to be very impractical at larger levels very quickly. :/ $\endgroup$ – Neil Mar 4 '16 at 13:13
  • $\begingroup$ My question is not necessarly to implement it, but to wonder if there could be an equivalent (or approaching) formulation in a way that would be easier to understand (at least for me). $\endgroup$ – Colin Pitrat Mar 4 '16 at 13:15

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