João Maguño and Lee Smolin propose a modification to special relativity where the Planck energy, in addition to the speed of light, becomes an invariant. This is achieved by modifying the action of the Lorentz group on momentum space, specifically by adding a dilatation to each boost while ensuring the Planck energy remains invariant. The modified algebra retains its original structure constants, and the group action is shown to be similar to a transformation previously proposed by Fock. The authors discuss the implications for field theory and suggest a modified equivalence principle to embed the new theory within general relativity. They emphasize that this modification preserves the relativity of inertial frames and the equivalence principle while incorporating the Planck scale as an invariant energy scale. The modified transformations are non-linear and act on momentum space, leading to new invariants and dispersion relations for particles. The authors also explore the potential experimental signatures of these modifications, particularly in ultra-high-energy cosmic rays and gamma ray bursts.João Maguño and Lee Smolin propose a modification to special relativity where the Planck energy, in addition to the speed of light, becomes an invariant. This is achieved by modifying the action of the Lorentz group on momentum space, specifically by adding a dilatation to each boost while ensuring the Planck energy remains invariant. The modified algebra retains its original structure constants, and the group action is shown to be similar to a transformation previously proposed by Fock. The authors discuss the implications for field theory and suggest a modified equivalence principle to embed the new theory within general relativity. They emphasize that this modification preserves the relativity of inertial frames and the equivalence principle while incorporating the Planck scale as an invariant energy scale. The modified transformations are non-linear and act on momentum space, leading to new invariants and dispersion relations for particles. The authors also explore the potential experimental signatures of these modifications, particularly in ultra-high-energy cosmic rays and gamma ray bursts.