A fibre-bundle model with dual spacetimes (smooth manifold plus causal set) derives relative locality in general PQG theories without requiring momentum-space curvature.
Amelino-Camelia, Relativity in space-times with short distance structure governed by an observer independent (Planckian) length scale, Int
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abstract
I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of space-times whose short-distance structure is governed by an observer-independent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type $E^2- c^2 p^2- c^4 m^2 + f(E,p,m;L_p)=0$, at least for certain types of $f$.
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In the classical basis the non-bijective momentum map induces branch-dependent κ-deformed back-to-back correlations for two-particle states obeying vanishing total momentum.
In the DSR1 model with subluminal light-speed variation, a boosted box can overtake its own emitted photon above a critical rapidity, leading to tensions in particle counting and motion not resolved by relative locality.
citing papers explorer
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Generalized relative locality and causal sets
A fibre-bundle model with dual spacetimes (smooth manifold plus causal set) derives relative locality in general PQG theories without requiring momentum-space curvature.
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Kinematical correlations via $\kappa$-Poincar\'e coproducts
In the classical basis the non-bijective momentum map induces branch-dependent κ-deformed back-to-back correlations for two-particle states obeying vanishing total momentum.
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On the Consistency of Covariant Light-Speed Variation in Doubly Special Relativity
In the DSR1 model with subluminal light-speed variation, a boosted box can overtake its own emitted photon above a critical rapidity, leading to tensions in particle counting and motion not resolved by relative locality.