Doubly special relativity

Short description: Generalization of special relativity

Doubly special relativity[1][2] (DSR) – also called deformed special relativity – is a modified theory of special relativity in which there is not only an observer-independent maximum velocity (the speed of light), but also an observer-independent maximum energy scale (the Planck energy) and/or a minimum length scale (the Planck length).[3] This contrasts with other Lorentz-violating theories, such as the Standard-Model Extension, where Lorentz invariance is instead broken by the presence of a preferred frame. The main motivation for this theory is that the Planck energy should be the scale where as yet unknown quantum gravity effects become important and, due to invariance of physical laws, this scale should remain fixed in all inertial frames.[4]

## Contents

* 1 History
* 2 De Sitter relativity
* 3 See also
* 4 References
* 5 Further reading

## History

First attempts to modify special relativity by introducing an observer-independent length were made by Pavlopoulos (1967), who estimated this length at about 10−15 metres.[5][6] In the context of quantum gravity, Giovanni Amelino-Camelia (2000) introduced what is now called doubly special relativity, by proposing a specific realization of preserving invariance of the Planck length 1.616255×10−35 m.[7][8] This was reformulated by Kowalski-Glikman (2001) in terms of an observer-independent Planck mass.[9] A different model, inspired by that of Amelino-Camelia, was proposed in 2001 by João Magueijo and Lee Smolin, who also focused on the invariance of Planck energy.[10][11]

It was realized that there are, indeed, three kinds of deformation of special relativity that allow one to achieve an invariance of the Planck energy; either as a maximum energy, as a maximal momentum, or both. DSR models are possibly related to loop quantum gravity in 2+1 dimensions (two space, one time), and it has been conjectured that a relation also exists in 3+1 dimensions.[12][13]

The motivation for these proposals is mainly theoretical, based on the following observation: The Planck energy is expected to play a fundamental role in a theory of quantum gravity; setting the scale at which quantum gravity effects cannot be neglected and new phenomena might become important. If special relativity is to hold up exactly to this scale, different observers would observe quantum gravity effects at different scales, due to the Lorentz–FitzGerald contraction, in contradiction to the principle that all inertial observers should be able to describe phenomena by the same physical laws. This motivation has been criticized, on the grounds that the result of a Lorentz transformation does not itself constitute an observable phenomenon.[4] DSR also suffers from several inconsistencies in formulation that have yet to be resolved.[14]Cite error: Closing `</ref>` missing for `<ref>` tag However, the Fermi-LAT experiment in 2009 measured a 31 GeV photon, which nearly simultaneously arrived with other photons from the same burst, which excluded such dispersion effects even above the Planck energy.[15] Moreover, it has been argued that DSR, with an energy-dependent speed of light, is inconsistent and first order effects are ruled out already because they would lead to non-local particle interactions that would long have been observed in particle physics experiments.[16]

## De Sitter relativity

Since the de Sitter group naturally incorporates an invariant length parameter, de Sitter relativity can be interpreted as an example of doubly special relativity because de Sitter spacetime incorporates invariant velocity, as well as length parameter. There is a fundamental difference, though: whereas in all doubly special relativity models the Lorentz symmetry is violated, in de Sitter relativity it remains as a physical symmetry. A drawback of the usual doubly special relativity models is that they are valid only at the energy scales where ordinary special relativity is supposed to break down, giving rise to a patchwork relativity. On the other hand, de Sitter relativity is found to be invariant under a simultaneous re-scaling of mass, energy and momentum, and is consequently valid at all energy scales.

## See also

* Planck scale
* Planck units
* Planck epoch
* Fock–Lorentz symmetry

## References

1. ↑ Amelino-Camelia, Giovanni (1 November 2009). "Doubly-Special Relativity: Facts, Myths and Some Key Open Issues". Recent Developments in Theoretical Physics. Statistical Science and Interdisciplinary Research. 9. pp. 123–170. doi:10.1142/9789814287333_0006. ISBN 978-981-4287-32-6.
2. ↑ Amelino-Camelia, Giovanni (1 July 2002). "Doubly Special Relativity". Nature 418 (6893): 34–35. doi:10.1038/418034a. PMID 12097897. Bibcode: 2002Natur.418...34A.
3. ↑ Amelino-Camelia, Giovanni (2010). "Doubly-Special Relativity: Facts, Myths and Some Key Open Issues". Symmetry 2 (4): 230–271. doi:10.3390/sym2010230. Bibcode: 2010rdtp.book..123A.
4. ↑ 4.0 4.1 Hossenfelder, S. (2006). "Interpretation of Quantum Field Theories with a Minimal Length Scale". Physical Review D 73 (10). doi:10.1103/PhysRevD.73.105013. Bibcode: 2006PhRvD..73j5013H.
5. ↑ Pavlopoulos, T. G. (1967). "Breakdown of Lorentz Invariance". Physical Review 159 (5): 1106–1110. doi:10.1103/PhysRev.159.1106. Bibcode: 1967PhRv..159.1106P.
6. ↑ Pavlopoulos, T. G. (2005). "Are we observing Lorentz violation in gamma ray bursts?". Physics Letters B 625 (1–2): 13–18. doi:10.1016/j.physletb.2005.08.064. Bibcode: 2005PhLB..625...13P.
7. ↑ Amelino-Camelia, Giovanni (2001). "Testable scenario for relativity with minimum length". Physics Letters B 510 (1–4): 255–263. doi:10.1016/S0370-2693(01)00506-8. Bibcode: 2001PhLB..510..255A.
8. ↑ Amelino-Camelia, Giovanni (2002). "Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale". International Journal of Modern Physics D 11 (1): 35–59. doi:10.1142/S0218271802001330. Bibcode: 2002IJMPD..11...35A.
9. ↑ Kowalski-Glikman, J. (2001). "Observer-independent quantum of mass". Physics Letters A 286 (6): 391–394. doi:10.1016/S0375-9601(01)00465-0. Bibcode: 2001PhLA..286..391K.
10. ↑ Magueijo, J.; Smolin, L. (2002). "Lorentz invariance with an invariant energy scale". Physical Review Letters 88 (19). doi:10.1103/PhysRevLett.88.190403. PMID 12005620. Bibcode: 2002PhRvL..88s0403M.
11. ↑ Magueijo, J.; Smolin, L. (2003). "Generalized Lorentz invariance with an invariant energy scale". Physical Review D 67 (4). doi:10.1103/PhysRevD.67.044017. Bibcode: 2003PhRvD..67d4017M.
12. ↑ Amelino-Camelia, Giovanni; Smolin, Lee; Starodubtsev, Artem (2004). "Quantum symmetry, the cosmological constant and Planck-scale phenomenology". Classical and Quantum Gravity 21 (13): 3095–3110. doi:10.1088/0264-9381/21/13/002. Bibcode: 2004CQGra..21.3095A.
13. ↑ Freidel, Laurent; Kowalski-Glikman, Jerzy; Smolin, Lee (2004). "2+1 gravity and doubly special relativity". Physical Review D 69 (4). doi:10.1103/PhysRevD.69.044001. Bibcode: 2004PhRvD..69d4001F.
14. ↑ Aloisio, R.; Galante, A.; Grillo, A. F.; Luzio, E.; Mendez, F. (2004). "Approaching Space Time Through Velocity in Doubly Special Relativity". Physical Review D 70 (12). doi:10.1103/PhysRevD.70.125012. Bibcode: 2004PhRvD..70l5012A.
15. ↑ Fermi LAT Collaboration (2009). "A limit on the variation of the speed of light arising from quantum gravity effects". Nature 462 (7271): 331–334. doi:10.1038/nature08574. PMID 19865083. Bibcode: 2009Natur.462..331A.
16. ↑ Hossenfelder, S. (2009). "The Box-Problem in Deformed Special Relativity". arXiv:0912.0090 [gr-qc].

## Further reading

* Amelino-Camelia, Giovanni (2002). "Doubly-Special Relativity: First Results and Key Open Problems". International Journal of Modern Physics D 11 (10): 1643-1669. doi:10.1142/S021827180200302X. Bibcode: 2002IJMPD..11.1643A.
* Amelino-Camelia, Giovanni (2002). "Relativity: Special treatment". Nature 418 (6893): 34–35. doi:10.1038/418034a. PMID 12097897. Bibcode: 2002Natur.418...34A.
* Energy and Geometry: An Introduction to Deformed Special Relativity. World Scientific. 2004. ISBN 981-238-728-5.
* Jafari, N.; Shariati, A. (2006). "Doubly Special Relativity: A New Relativity or Not?". 841. pp. 462-465. doi:10.1063/1.2218214.
* Kowalski-Glikman, J. (2005). "Introduction to Doubly Special Relativity". Planck Scale Effects in Astrophysics and Cosmology. Lecture Notes in Physics. 669. pp. 131-159. doi:10.1007/b105189. ISBN 978-3-540-25263-4.
* Smolin, Lee (2006). "Chapter 14. Building on Einstein". The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. Boston, Massachusetts: Houghton Mifflin. ISBN 978-0-618-55105-7. OCLC 64453453. Smolin writes for the layman a brief history of the development of DSR and how it ties in with string theory and cosmology.

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