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So imagine space is a regular square mesh or lattice. In a theory like QCD, the photon lines are placed along the edges of this graph to form paths.

The space is supposed to represent simple Minkowksi space in the limit when the lattice points approach zero.

So what would a graviton (a quanta of curvature) be like in this picture?

I had a thought that graviton paths could be "off-grid". i.e. the paths of the gravitons would be new lines that intersect the graph at midpoints of the edges thereby creating new vertices in the graph and more "space-time". And photons could even move along these new lines and vertices. All particles would emit these graviton lines and hence create more space-time vertices near themselves, giving apparent curvature.

enter image description here

In more than 2+1 dimensions, one could imagine tubes that go through the graph and intersect the vertices in the graph creating additional vertices and edges.

enter image description here

Therefor if you had a lot of these graviton paths this would create a lot more vertices and edges creating additional space-time volume in that area giving the appearance of curvature.

Or alternatively there might be special "graph rules" for how these localised "gravitons" move about the grid. e.g:

enter image description here

Well, anyway, the point of this being is that, is this a way that one can have gravitons which are like particles but also like localised areas of space-time curvature? (And is this necessary?)

One problem is that we are starting with a mesh which is like background of interacting gravitons. (Just replace the black lines with blue lines!) And we have to explain why this is an acceptable background to start with.

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    $\begingroup$ This seems like a personal non-mainstream theory unless you provide some references. $\endgroup$
    – A.V.S.
    Commented May 25, 2020 at 6:10

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If you're hoping for a lattice description of graviton modes from a lattice description. Maybe you should check the work of Profesor Xiao-Gang Wen

Emergence of helicity +/- 2 modes (gravitons) from qubit models

Overview talk

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  • $\begingroup$ Thanks! I'll check it out! $\endgroup$
    – user84158
    Commented Jun 2, 2020 at 18:31
  • $\begingroup$ Glad that the answer served you. You could also check this gentle overview of Wen's quibit models. You could find there qubit lattice models for photons or even discrete models for Emergent Kalb-Ramond Fields or mimetic dark matter. $\endgroup$
    – Ramiro Hum-Sah
    Commented Jun 2, 2020 at 20:08