Compare · The Nature of Space & Time

Relative Locality vs Magueijo-Smolin Doubly Special Relativity

Deformed Special Relativity · within family

	Relative Locality Speculative	Magueijo-Smolin Doubly Special Relativity Speculative
Proposed	2011	2002
Key figures	Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin	João Magueijo, Lee Smolin
In one sentence	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.	A modified special relativity in which the Planck energy joins the speed of light as an invariant, while all inertial frames stay equivalent and Einstein's theory returns at low energies.
Predictions	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	Every inertial observer measures the same Planck-scale energy, alongside the same speed of light Physics agrees with special relativity at energies far below the invariant scale In some versions of the 2003 generalization, elementary particles have a maximum momentum or energy and the speed of light varies with energy Field theory and the equivalence principle are modified, with consequences for how the theory might embed in [[general relativity]]
Where it breaks	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.	The 2003 generalization admits many examples with different maximum energies and photon speeds, so the framework alone does not fix one prediction. Versions with a speed of light that changes at first order in energy over the Planck energy face the Fermi and LHAASO gamma-ray burst limits. The 2002 paper only suggests a modified equivalence principle, so a full gravitational version of the model was left for later work.
Key unresolved problem	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.	Choosing which of the many allowed non-linear boosts is physical, since each choice changes the maximum energy and how the speed of light behaves.
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Relative Locality

2011 · Speculative

Magueijo-Smolin Doubly Special Relativity

2002 · Speculative

Proposed

2011

2002

Key figures

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

João Magueijo, Lee Smolin

In one sentence

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.

A modified special relativity in which the Planck energy joins the speed of light as an invariant, while all inertial frames stay equivalent and Einstein's theory returns at low energies.

Predictions

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

Every inertial observer measures the same Planck-scale energy, alongside the same speed of light
Physics agrees with special relativity at energies far below the invariant scale
In some versions of the 2003 generalization, elementary particles have a maximum momentum or energy and the speed of light varies with energy
Field theory and the equivalence principle are modified, with consequences for how the theory might embed in [[general relativity]]

Where it breaks

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.

The 2003 generalization admits many examples with different maximum energies and photon speeds, so the framework alone does not fix one prediction.
Versions with a speed of light that changes at first order in energy over the Planck energy face the Fermi and LHAASO gamma-ray burst limits.
The 2002 paper only suggests a modified equivalence principle, so a full gravitational version of the model was left for later work.

Key unresolved problem

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.

Choosing which of the many allowed non-linear boosts is physical, since each choice changes the maximum energy and how the speed of light behaves.

Reader vote

No votes yet