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Magueijo-Smolin Doubly Special Relativity vs Amelino-Camelia's Doubly Special Relativity

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Deformed Special Relativity · within family

	Magueijo-Smolin Doubly Special Relativity Speculative	Amelino-Camelia's Doubly Special Relativity Speculative
Proposed	2002	2002
Key figures	João Magueijo, Lee Smolin	Giovanni Amelino-Camelia
In one sentence	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.	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.
Predictions	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]]	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
Where it breaks	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.	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.
Key unresolved problem	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.	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.
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Magueijo-Smolin Doubly Special Relativity

2002 · Speculative

Amelino-Camelia's Doubly Special Relativity

2002 · Speculative

Proposed

2002

Key figures

João Magueijo, Lee Smolin

Giovanni Amelino-Camelia

In one sentence

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.

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.

Predictions

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]]

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

Where it breaks

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.

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.

Key unresolved problem

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.

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.

Reader vote

No votes yet