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Does the notion of blurriness of lightcone appear in any theory of quantum gravity?

Physics Asked on April 18, 2021

light cone

In the above diagram, black lines are $x=pm t$ and the highlighted space is what I meant by the blurriness of the lightcone.

Personally I have 2 arguments and both seems to suggest there shouldn’t be any blurriness.

  • In GR regime the light cones are there not because of some property of massless particles but because
    of the intrinsic nature of the geometry of spacetime.
  • Though in Quantum mechanics the particle can’t be localized, even the
    $hat{x}$ eigenvectors spread over time. In QFT we use distribution
    function to force $[hat{O}(x),hat{O}(y)]=0$ for $(x-y)^2<0$, signature is $(+,-,-,-)$. But such distribution are ill-behaved at very small distance

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