Determine the physically correct Planck-scale dispersion relation

Determine the physically correct modified dispersion relation describing particle kinematics in nature among the non-unique dispersion relations proposed within doubly special relativity, using experimental evidence.

Background

The paper adopts the Magueijo–Smolin doubly special relativity model and uses the modified dispersion relation E² − p² = m²(1 − E/Λ)², with Λ identified as the Planck energy. The authors emphasize that this choice is not uniquely determined by the DSR framework. Consequently, selecting the physically realized relation is an unresolved empirical problem with direct implications for predictions of Planck-scale thermodynamics, photon propagation, and other quantum-gravity phenomenology.

References

We emphasize that the choice of this dispersion relation is not unique, only experiments can determine the correct dispersion relation in nature.

— Photon Gas Thermodynamics with $κ$-generalized statistics at Planck-Scale  (2609.00606 - Yang et al., 1 Sep 2026) in Section II, “DSR and Modified Disperse Relation”