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We typically draw light-cones to study causal relation between two space-time points.

Source : Wikipedia

Space-Time is manifest as the metric in various calculations. If one considers that something like Quantum Gravity does indeed exist then shouldn't the quantum fluctuations in metric make the sharp-lines of light-cones a little bit fuzzy? Basically implying that the boundary of light-cone is not sharp i.e. it has non-zero finite thickness. Boundary here corresponds to the null rays.

Does that make sense? Is there any indicative literature where this has been studied or some approach to study this?

I don't think this is considered while doing any semi-classical analysis where the metric is taken to be a classical background with quantum fields defined on points of it.

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    $\begingroup$ related https://physics.stackexchange.com/q/569232 $\endgroup$
    – aitfel
    Commented Sep 8, 2020 at 16:45
  • $\begingroup$ Please note that the related question is also unanswered. @aitfel Thanks a lot for pointing out that question. It is really interesting to see that you had the exact same thought as me. Now I find it much easier to believe that people can independently discover similar things around same time $\endgroup$
    – self.grassmanian
    Commented Sep 9, 2020 at 11:07
  • $\begingroup$ Not sure if this is what you're asking, but this reminds me of something I encountered in QFT. Basically, the propagator of, say, a scalar field theory is non-zero even for spacelike seperated points (the fuzziness you're talking about reminded me of this point). But when you calculate the commutator of spacelike seperated fields, you find that the contributions from the propagators cancel out to give zero. This means that there should be no observable consequence of some perturbation on points which are spacelike separated from the point you perturbed. $\endgroup$
    – thunderbolt
    Commented Sep 10, 2020 at 9:00
  • $\begingroup$ @thunderbolt You are correct, that is not what I am asking. My question pertains to the area of Quantum Gravity where along with quantum theory you also have to consider gravity. $\endgroup$
    – self.grassmanian
    Commented Sep 10, 2020 at 11:27

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