• In LQG, does spacetime consist of interconnected loops?
  • Are those loops real?
  • If spacetime does not consist of the aforementioned loops, what it consists of?

The definition of real would be: they physically exist. I don't know if this helps, but for me things that physically exist would be for example an atom, a rock, a book,.. I hope you get my meaning.

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    $\begingroup$ Define "real" in your second question. $\endgroup$ – Kyle Kanos Apr 6 '15 at 23:55
  • $\begingroup$ As far as I know, the Wilson loops are a computational device and not intended to be a fundamental unit of spacetime. Likewise the spin networks/foams that have superceded the use of Wilson loops. I would be interested to see a definitive statement on the subject, though I don't know whether we have any LQGers amongst the active site members at the moment. $\endgroup$ – John Rennie Apr 7 '15 at 5:23
  • $\begingroup$ @JohnRennie what about Carlo Rovelli? $\endgroup$ – Stan Shunpike Apr 9 '15 at 5:22
  • $\begingroup$ @StanShunpike: Carlo Rovelli was last on the site four years ago. That's not very active. $\endgroup$ – John Rennie Apr 9 '15 at 7:15
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    $\begingroup$ I'm a bit surprised at the *Unclear what you're asking" close votes. It seems obvious what Mick is asking (though it's not at all clear to me that the answer is obvious). $\endgroup$ – John Rennie Apr 9 '15 at 7:17

States in loop quantum gravity are the cylindrical functions, i. e. functions associated to edges and knots on a triangulated manifold. Such triangulated manifolds define the discretised space-time upon which the states (defined as above) are supposed to close a Hilbert space once a suitable scalar product is defined.

Hamiltonians, Lagrangians and all the rest can be defined starting from the corresponding Einstein-Hilbert actions and performing some sort of discretisations thereupon.

Have a look at this other answer of mine for a broader insight and links therein to the corresponding literature. Of course, though, the complete subject is much more complicated, but this is the general underlying idea.


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