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I've read Rovelli's book and papers, but he makes little mention of quantum fields. What is the interaction between fields and his particulate space of loop quantum gravity? I know that he says loop quantum gravity "is space", so would fields then ride above that and be "in space". I'm thinking of space as a bowl full of salt, and then a field as being jello poured into the bowl and filling up the gaps?

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  • $\begingroup$ I must say I've never heard the analogy of space as a bowl full of salt and fields being jello poured into the bowl... I'm not sure how I feel about this. But anyway, Rovelli usually speaks only about fields, famously: "No more fields on spacetime: just fields on fields", and hence the relations between these fields without a background spacetime to work on. I'm not sure if this is in line with your interpretation? $\endgroup$
    – Eletie
    Commented Dec 21, 2020 at 18:42
  • $\begingroup$ Another quote, just from the Wiki, which may be in disagreement (or not) with your interpretation: space-time as a "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world $\endgroup$
    – Eletie
    Commented Dec 21, 2020 at 18:45
  • $\begingroup$ @Eletie Rovelli's theory has a very definite particulate nature to it. A bowl of salt is just the best visualization I can come up with . And he is very definite that this "is space", not in space or on space. I'm more interested with how energy would be exchanged between the two. $\endgroup$ Commented Dec 21, 2020 at 20:38
  • $\begingroup$ (small point, LQG is of course not 'Rovelli's'). I was also joking about the analogy. As to your other question, in LQG the quantum field of gravity acts in the same fashion as the other quantum fields. I'm not sure what you mean by energy, as that's a very specific term which is hard enough to define even in GR. Rovelli's monograph on Quantum Gravity gives a good introduction to the topic as well as a recap on GR and QFT. I'm unsure though how having read Rovelli's work you say he makes little mention to quantum fields, as this is really all his work talks about?! $\endgroup$
    – Eletie
    Commented Dec 21, 2020 at 20:55
  • $\begingroup$ @Eletie I was definitely not thinking of the gravitational field, because it is really the gravitational field that we are working to define with LQG. Rather, I'm wondering about the other quantum fields, like the quark field, electromagnetic field, etc. How do they interact with LQG? $\endgroup$ Commented Dec 21, 2020 at 23:58

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LQG is a specific flavor of the quantization procedure applied to General Relativity. You can apply the same procedure to a system of GR coupled to matter fields. You won't get a QFT in the usual sense, because there's no global Poincare invariance, because space-time is dynamical. But there will be a sector in the theory that will closely resemble QFT particles on the Minkowski background interacting with each other, and with weak gravity.

Unlike string theory, LQG doesn't attempt to unify matter and gravity – just to consistently quantize a coupled system. Though there have been proposals on how quantum fields / particles may originate from quantum aspects of LQG's geometry (noiseless subsystems), however, those proposals are highly speculative and unsuccessful.

Rovelli actually quantizes GR + matter systems in his books, and there's plenty of material on the subject on arxiv, too.

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