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I have been studying quantum gravity theories. Many theories would have gravity (that is space and time) defined by the exchange of a gravitational quanta. That is simple in sense it is readily comprehensible. There are only effective field theories and stochastic field theories and whether the theories have been validated is debated by experts, so alternative ideas exist. I am trying to understand the idea behind loop gravity, which if I read correctly postulates a gravitational field which is a superposition of geometries. If that is correct it is not clear what particles exchange during gravitational interaction, when energy is transferred. Normally a geometry describes rules which describe the path of a mass less particle, keep all the rules of quantum field theory covariant under Lorentz group transformations, and maintain the co-variance of pseudo-Reimannian metric relevant to a given theory. If you have more than geometry in the sense just stated, do zero mass particles move at different speeds and do any two points in space time have multiple metrics describing their distance. If the answer is that the speed of light is not constant and there is not one metric describing space time intervals then how is the process properly described as having any geometry. Normally when a field is described as a superposition of multiple states it is assumed it can collapse to an eigen state. Is there a description of such a collapse or is superposition meant in a different sense. Bare in mind when a particle exists as superposition of 2 eigen states (highly coherent), both states can interact with other particles, but according to rules of geometry the results of all the interactions are Lorentz invariant. Multiple geometries would make this difficult to understand. It certainly forbids describing geometry as a results of supper positions of the states of the graviton. Observation so far has not identified several states of the graviton.

I am not suggesting there is problem with the loop approach (I would not be able to tell if there were), I am directly asking for an explanation. The universe may be difficult to understand, but I have looked at several sources and they do not address these questions. Most fields can be defined by spin and characters of how they couple to other fields (including gauge symmetries of the couplings and interaction with Higgs, rest mass). The loop approach seems to postulate a field that is different in fundamental sense, and I would like to understand that.

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My knowledge of LQG comes from my own study and limited so you should confirm elsewhere. I don't believe that LQG has a graviton. LQG origins can be traced back to spin networks. Imagine a world without space-time, just particles (quantum systems) that interact with each other and obey conservation laws (of spin in particular). As they interact, the possible interactions can be drawn in Feynman like diagrams. Spin networks naturally define 3D directions between large islands of spin; the result is an emergent form of space-time (superimposition of "geometries" implied by spin-networks). Loops also evolve naturally from this description, however I'm not really competent to comment much beyond this point.

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  • $\begingroup$ I assume you mean that there is some kind of S matrix, and you can draw Feynman diagrams, and with great difficulty, derive Feynman rules describing the interaction. So, I should be able to find references to both graphs and associated rules, which might answer my question. $\endgroup$ – yeaton Jan 15 at 22:28

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