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Amelino-Camelia's Doubly Special Relativity vs Relative Locality

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Deformed Special Relativity · within family

	Amelino-Camelia's Doubly Special Relativity Speculative	Relative Locality Speculative
Proposed	2002	2011
Key figures	Giovanni Amelino-Camelia	Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin
In one sentence	The rules of special relativity can be rewritten so that all inertial observers agree on a Planck-scale length, without picking out any preferred frame.	The shared arena of physics is phase space, and each observer builds a spacetime from it, so distant observers can disagree about whether an interaction happened at a single point.
Predictions	All inertial observers agree on a Planck-scale length as well as on the speed of light, and no preferred frame exists Energy, momentum and mass obey a deformed relation with Planck-length corrections, and every observer finds the same relation In particular κ-Poincaré realizations, boosts saturate at a maximum momentum equal to the inverse Planck length If the deformation makes photon speed depend on energy, high-energy gamma rays from distant bursts arrive at different times than low-energy ones	Momentum space has a geometry set by the Planck mass, which can modify how energy and momentum are defined and conserved These deformations of the conservation laws are in principle measurable by appropriate experiments An interaction that is local for a nearby observer appears non-local to a distant one, by an amount tied to the energies involved, while locality is kept in phase space Astrophysical observations could measure the geometry of momentum space
Where it breaks	The 2002 paper proves consistency for certain types of deformation only, so the general case is still open. Fermi's 2009 limit from GRB 090510 disfavours versions in which photon speed changes linearly with energy at the Planck scale. The framework allows several deformations. Amelino-Camelia's own 2010 review describes DSR scenarios with and without a modified dispersion relation, so one null result rules out only some versions.	Giving up absolutely coincident events is a large conceptual price. Hossenfelder argued in 2010 that models with an energy-dependent speed of light produce non-locality that conflicts with known particle physics, and later work tried to answer her. Curvature, torsion and non-metricity are free choices, so the geometry of momentum space rests on extra physical hypotheses instead of a derivation. The principle is formulated for a regime in which Planck's constant and Newton's constant are neglected, so its link to a full quantum theory of gravity is still missing.
Key unresolved problem	Which deformation nature uses, if any: the postulates allow several, and the version with a linear photon delay is already squeezed by gamma-ray burst data.	Deriving the geometry of momentum space from an actual theory of quantum gravity, so that its curvature and torsion are fixed by theory and can be compared with data.
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Amelino-Camelia's Doubly Special Relativity

2002 · Speculative

Relative Locality

2011 · Speculative

Proposed

2002

2011

Key figures

Giovanni Amelino-Camelia

Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin

In one sentence

The rules of special relativity can be rewritten so that all inertial observers agree on a Planck-scale length, without picking out any preferred frame.

The shared arena of physics is phase space, and each observer builds a spacetime from it, so distant observers can disagree about whether an interaction happened at a single point.

Predictions

All inertial observers agree on a Planck-scale length as well as on the speed of light, and no preferred frame exists
Energy, momentum and mass obey a deformed relation with Planck-length corrections, and every observer finds the same relation
In particular κ-Poincaré realizations, boosts saturate at a maximum momentum equal to the inverse Planck length
If the deformation makes photon speed depend on energy, high-energy gamma rays from distant bursts arrive at different times than low-energy ones

Momentum space has a geometry set by the Planck mass, which can modify how energy and momentum are defined and conserved
These deformations of the conservation laws are in principle measurable by appropriate experiments
An interaction that is local for a nearby observer appears non-local to a distant one, by an amount tied to the energies involved, while locality is kept in phase space
Astrophysical observations could measure the geometry of momentum space

Where it breaks

The 2002 paper proves consistency for certain types of deformation only, so the general case is still open.
Fermi's 2009 limit from GRB 090510 disfavours versions in which photon speed changes linearly with energy at the Planck scale.
The framework allows several deformations. Amelino-Camelia's own 2010 review describes DSR scenarios with and without a modified dispersion relation, so one null result rules out only some versions.

Giving up absolutely coincident events is a large conceptual price. Hossenfelder argued in 2010 that models with an energy-dependent speed of light produce non-locality that conflicts with known particle physics, and later work tried to answer her.
Curvature, torsion and non-metricity are free choices, so the geometry of momentum space rests on extra physical hypotheses instead of a derivation.
The principle is formulated for a regime in which Planck's constant and Newton's constant are neglected, so its link to a full quantum theory of gravity is still missing.

Key unresolved problem

Which deformation nature uses, if any: the postulates allow several, and the version with a linear photon delay is already squeezed by gamma-ray burst data.

Deriving the geometry of momentum space from an actual theory of quantum gravity, so that its curvature and torsion are fixed by theory and can be compared with data.

Reader vote

No votes yet