This paper proposes a modification of special relativity in which the Planck energy becomes an invariant, alongside the speed of light, while preserving the relativity of inertial frames and agreeing with Einstein's theory at low energies. This is achieved by modifying the action of the Lorentz group on momentum space, adding a dilatation to each boost to ensure the Planck energy remains invariant. The resulting algebra retains the same structure constants, and the group action is similar to a transformation previously proposed by Fock.
The paper addresses the paradox of determining the reference frame in which the Planck scale is the threshold for new quantum spacetime phenomena. It argues that Lorentz invariance can be preserved while incorporating the Planck scale into physics, ensuring that all observers agree on the Planck scale as the threshold for quantum spacetime transitions. This is done by modifying the action of the Lorentz group on momentum space, leading to a non-linear representation that preserves the Planck energy.
The paper discusses the implications for field theory, suggesting modifications to the equivalence principle and how the new theory could be embedded in general relativity. It also explores the non-linear representation of the Lorentz group, showing how it acts on momentum space and leads to modified transformations for particles and photons. The paper highlights the invariance of the Planck energy and the resulting modifications to the usual quadratic invariant on momentum space.
The paper also considers the implications for gravitational redshift and the equivalence principle, showing how the modified theory could lead to a consistent modification of general relativity. It raises questions about extending the modified Lorentz group action to spinor fields, supersymmetry, and string theory, and whether the proposed principles can be derived from causal spin foam models. The paper concludes by noting that the proposed modification of special relativity is consistent with the relativity of inertial frames and the equivalence principle, while preserving the Planck energy as an invariant.This paper proposes a modification of special relativity in which the Planck energy becomes an invariant, alongside the speed of light, while preserving the relativity of inertial frames and agreeing with Einstein's theory at low energies. This is achieved by modifying the action of the Lorentz group on momentum space, adding a dilatation to each boost to ensure the Planck energy remains invariant. The resulting algebra retains the same structure constants, and the group action is similar to a transformation previously proposed by Fock.
The paper addresses the paradox of determining the reference frame in which the Planck scale is the threshold for new quantum spacetime phenomena. It argues that Lorentz invariance can be preserved while incorporating the Planck scale into physics, ensuring that all observers agree on the Planck scale as the threshold for quantum spacetime transitions. This is done by modifying the action of the Lorentz group on momentum space, leading to a non-linear representation that preserves the Planck energy.
The paper discusses the implications for field theory, suggesting modifications to the equivalence principle and how the new theory could be embedded in general relativity. It also explores the non-linear representation of the Lorentz group, showing how it acts on momentum space and leads to modified transformations for particles and photons. The paper highlights the invariance of the Planck energy and the resulting modifications to the usual quadratic invariant on momentum space.
The paper also considers the implications for gravitational redshift and the equivalence principle, showing how the modified theory could lead to a consistent modification of general relativity. It raises questions about extending the modified Lorentz group action to spinor fields, supersymmetry, and string theory, and whether the proposed principles can be derived from causal spin foam models. The paper concludes by noting that the proposed modification of special relativity is consistent with the relativity of inertial frames and the equivalence principle, while preserving the Planck energy as an invariant.