Editing Doubly special relativity (section)

==History==
First attempts to modify special relativity by introducing an observer-independent length were made by Pavlopoulos (1967), who estimated this length at about {{val||e=-15|u=[[metre]]s}}.<ref>{{Cite journal |author=Pavlopoulos, T. G. |title=Breakdown of Lorentz Invariance |journal=Physical Review |volume=159 |issue=5 |pages=1106–1110 |year=1967 |doi=10.1103/PhysRev.159.1106 |bibcode=1967PhRv..159.1106P}}</ref><ref>{{Cite journal |author=Pavlopoulos, T. G. |title=Are we observing Lorentz violation in gamma ray bursts? |journal=Physics Letters B |volume=625 |issue=1–2 |pages=13–18 |year=2005 |doi=10.1016/j.physletb.2005.08.064 |bibcode=2005PhLB..625...13P|arxiv=astro-ph/0508294|s2cid=609286 }}</ref> 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]] {{val|1.616255|e=-35|u=m}}.<ref>{{Cite journal |author=Amelino-Camelia |first=Giovanni |year=2001 |title=Testable scenario for relativity with minimum length |journal=Physics Letters B |volume=510 |issue=1–4 |pages=255–263 |arxiv=hep-th/0012238 |bibcode=2001PhLB..510..255A |doi=10.1016/S0370-2693(01)00506-8 |s2cid=119447462}}</ref><ref>{{Cite journal |author=Amelino-Camelia |first=Giovanni |year=2002 |title=Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale |journal=International Journal of Modern Physics D |volume=11 |issue=1 |pages=35–59 |arxiv=gr-qc/0012051 |bibcode=2002IJMPD..11...35A |doi=10.1142/S0218271802001330 |s2cid=16161466}}</ref> This was reformulated by Kowalski-Glikman (2001) in terms of an observer-independent [[Planck mass]].<ref>{{Cite journal |author=Kowalski-Glikman, J.  |title=Observer-independent quantum of mass |journal=Physics Letters A |volume=286 |issue=6 |pages=391–394 |year=2001 |arxiv=hep-th/0102098 |doi=10.1016/S0375-9601(01)00465-0|bibcode = 2001PhLA..286..391K |s2cid=118984500 }}</ref> 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]].<ref>{{Cite journal |author1=Magueijo |first=J. |author2=Smolin |first2=L. |year=2002 |title=Lorentz invariance with an invariant energy scale |journal=Physical Review Letters |volume=88 |issue=19 |pages=190403 |arxiv=hep-th/0112090 |bibcode=2002PhRvL..88s0403M |doi=10.1103/PhysRevLett.88.190403 |pmid=12005620 |s2cid=14468105}}</ref><ref>{{Cite journal |author1=Magueijo |first=J. |author2=Smolin |first2=L. |year=2003 |title=Generalized Lorentz invariance with an invariant energy scale |journal=Physical Review D |volume=67 |issue=4 |pages=044017 |arxiv=gr-qc/0207085 |bibcode=2003PhRvD..67d4017M |doi=10.1103/PhysRevD.67.044017 |s2cid=16998340}}</ref>

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.<ref>{{Cite journal |author1=Amelino-Camelia, Giovanni |author2=Smolin, Lee |author3=Starodubtsev, Artem |title=Quantum symmetry, the cosmological constant and Planck-scale phenomenology |journal=Classical and Quantum Gravity |volume=21 |issue=13 |pages=3095–3110 |year=2004 |arxiv=hep-th/0306134 |doi=10.1088/0264-9381/21/13/002|bibcode = 2004CQGra..21.3095A |s2cid=15024104 }}</ref><ref>{{Cite journal |author1=Freidel, Laurent |author2=Kowalski-Glikman, Jerzy |author3=Smolin, Lee |title=2+1 gravity and doubly special relativity |journal=Physical Review D |volume=69 |issue=4 |pages=044001 |year=2004 |arxiv=hep-th/0307085 |doi=10.1103/PhysRevD.69.044001|bibcode = 2004PhRvD..69d4001F |s2cid=119509057 }}</ref>

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.<ref name="Hossenfelder2006"/> DSR also suffers from several inconsistencies in formulation that have yet to be resolved.<ref name="Aloisio2004">
{{Cite journal |last1=Aloisio |first1=R. |last2=Galante |first2=A. |last3=Grillo |first3=A. F. |last4=Luzio |first4=E. |last5=Mendez |first5=F. |year=2004 |title=Approaching Space Time Through Velocity in Doubly Special Relativity |journal=[[Physical Review D]] |volume=70 |issue=12 |pages=125012 |arxiv=gr-qc/0410020 |bibcode=2004PhRvD..70l5012A |doi=10.1103/PhysRevD.70.125012 |s2cid=2111595}}</ref><ref name="Aloisio2005">
{{Cite journal
 |first1=R. |last1=Aloisio |first2=A. |last2=Galante |first3=A.F. |last3=Grillo
 |first4=E. |last4=Luzio |first5=F. |last5=Mendez
 |title=A note on DSR-like approach to space-time
 |journal=[[Physics Letters B]]
 |volume=610 |issue= 1–2|pages=101–106
 |year=2005
 |arxiv=gr-qc/0501079
 |doi=10.1016/j.physletb.2005.01.090
|bibcode = 2005PhLB..610..101A |s2cid=119346228 }}</ref> Most notably, it is difficult to recover the standard transformation behavior for macroscopic bodies, known as the soccer ball problem.<ref>{{Cite journal |last=Hossenfelder |first=Sabine |author-link=Sabine Hossenfelder |date=9 July 2014 |title=The Soccer-Ball Problem |url=http://www.emis.de/journals/SIGMA/2014/074/ |journal=Symmetry, Integrability and Geometry: Methods and Applications |volume=10 |pages=74 |arxiv=1403.2080 |bibcode=2014SIGMA..10..074H |doi=10.3842/SIGMA.2014.074 |s2cid=14373748 |access-date=16 April 2022 |archive-date=19 March 2022 |archive-url=https://web.archive.org/web/20220319004139/https://www.emis.de/journals/SIGMA/2014/074/ |url-status=live }}</ref> The other conceptual difficulty is that DSR is ''[[a priori]]'' formulated in [[momentum space]]. There is, as of yet, no consistent formulation of the model in [[position space]].