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| | Your wish maybe to really have a booming online business. Perhaps you have a little internet business today. Perhaps you have tried several online plans' that didn't work. Perhaps you are starting to consider what's available.<br><br> |
| {{lead too short|date=May 2012}}
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| '''Doubly special relativity''' (DSR) – also called '''deformed special relativity''' or, by some, '''extra-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 an observer-independent maximum energy scale and minimum length scale (the [[Planck energy]] and [[Planck length]]).<ref> | |
| {{Cite journal
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| |author=Amelino-Camelia, G.
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| |title=Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
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| |journal=Symmetry
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| |volume=2 |issue= |pages=230–271
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| |page=
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| |year=2010
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| |arxiv=1003.3942|bibcode = 2010arXiv1003.3942A }}</ref>
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| ==History==
| | E-Mail in their mind and keep your opt-in clients #'s increasing. Use autoresponders to take care of your campaigns. Then, you do not have to be there in person to advertise. That Is Clearly A success to utilize busy people! One bookcoaching customer, Jeanne offered 68 books the very first week she introduced in her ezine.It's OK to send the coupon out again and again -having a few changes and new data every time. At the bottom of the mail, send them to your site with a link where you offer the book.<br><br>Another favorite may be the receive money for reading e-mails. It is a natural Ponzi because nobody is obviously paying you to read them. You obtain paidfor recruiting others. Or there are the get paid for surveys we all have seen. Trouble is, in order to complete the review you have to sign up with a lot of sponsors, which if course all charge you. Yes you might actually receives a commission to take the survey, but youAre likely to spend a lot more than you produce. I truly did find one company that paid for reviews. I took 5 studies which required me to invest a bit over two and half-hours to complete. They sent me a check After complaining to the company for non payment. for $5.00. Nearly the big money I had been promised.<br><br><br><br>As much as there's that, it's also becoming more costly for companies to promote their items. Using The net they're many options available and some are every expensive and some are free.<br><br>+Time eating. [http://20thstreetblockparty.com/2014/jordan-kurland-intro/ Jordan Kurland] can be quite time intensive. Especially if you don't know what you're doing. One method to beat that is to obtain the proper tools to help you out.<br><br>I'm-not saying everyone reading this post is going out there and start their own delivery company that goes odd things but I do believe that everyone out there could carve out their own little niche. You'll realize that there are always a load of people searching for this online If you search for Shipment Wars Information. The same as there are a million people out there trying to find truly random garbage. If you're good at this, this crap can change into gold for you.<br><br>One method to promote your home based business is to utilize Pay-Per-Click (PPC). The style is that you just quote a particular amount on keywords associated with your company. You merely pay for traffic that really visits your web site.<br><br>No matter where you choose is the best location for you, make sure to talk with everyone. Do not communicate with them. As previously mentioned above, they'll be gone in a heartbeat if they dropped they're being marketed to. Do not you need to be that firm. Be a true person. Do not forget of showcasing some of your absolute best work, many effective weddings or content clients - especially with movies. Answer comments and questions seriously and interact in related teams. When you develop into a reliable person in the neighborhood you're in, you'll be surprised what social-media can-do to your wedding business. |
| First attempts to modify special relativity by introducing an observer independent length were made by Pavlopoulos (1967), who estimated this length to 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}}</ref>
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| In the context of [[quantum gravity]], [[Giovanni Amelino-Camelia]] (2000) introduced what now is called doubly special relativity, by proposing a specific realization of preserving invariance of the [[Planck length]] {{val|16.162|e=-36|u=m}}.<ref>{{Cite journal |author=Amelino-Camelia, G. |title=Testable scenario for relativity with minimum length |journal=Physics Letters B |volume=510 |issue=1-4 |pages=255–263 |year=2001 |arxiv=hep-th/0012238 |doi=10.1016/S0370-2693(01)00506-8|bibcode = 2001PhLB..510..255A }}</ref><ref>{{Cite journal |author=Amelino-Camelia, G. |title=Relativity in space–times with short-distance structure governed by an observer-independent (Planckian) length scale |journal=International Journal of Modern Physics D |volume=11 |issue=01 |pages=35–59 |page= |year=2002 |arxiv=gr-qc/0012051 |doi=10.1142/S0218271802001330 |bibcode=2002IJMPD..11...35A}}</ref>
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| 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 }}</ref>
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| 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 |author=Magueijo, J.; Smolin, L |title=Lorentz invariance with an invariant energy scale |journal=Physical Review Letters |volume=88 |issue=19 |pages=190403 |year=2001 |arxiv=hep-th/0112090 |doi=10.1103/PhysRevLett.88.190403 |bibcode=2002PhRvL..88s0403M}}</ref><ref>{{Cite journal |author=Magueijo, J.; Smolin, L |title=Generalized Lorentz invariance with an invariant energy scale |journal=Physical Review D |volume=67 |issue=4 |pages=044017 |year=2003 |arxiv=gr-qc/0207085 |doi=10.1103/PhysRevD.67.044017 |bibcode=2003PhRvD..67d4017M}}</ref>
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| It was realized that there are indeed three kind of deformations 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 |author=Amelino-Camelia, Giovanni; Smolin, Lee; 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 }}</ref><ref>{{Cite journal |author=Freidel, Laurent; Kowalski-Glikman, Jerzy; 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 }}</ref> | |
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| The motivation to 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">
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| {{Cite journal
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| |first=S. |last=Hossenfelder
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| |title=Interpretation of Quantum Field Theories with a Minimal Length Scale
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| |journal=[[Physical Review D]]
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| |volume=73 |issue= |pages= 105013|page=
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| |year=2006
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| |arxiv=hep-th/0603032
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| |doi=10.1103/PhysRevD.73.105013
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| |bibcode = 2006PhRvD..73j5013H }}</ref>
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| DSR also suffers from several inconsistencies in formulation that have yet to be resolved.<ref name="Aloisio2004">
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| {{Cite journal
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| |first=R. |last=Aloisio |first2=A. |last2=Galante |first3=A.F. |last3=Grillo
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| |first4=E. |last4=Luzio |first5=F. |last5=Mendez
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| |title=Approaching Space Time Through Velocity in Doubly Special Relativity
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| |journal=[[Physical Review D]]
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| |volume=70 |issue= |pages= 125012|page=
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| |year=2004
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| |arxiv=gr-qc/0410020
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| |doi=10.1103/PhysRevD.70.125012
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| |bibcode = 2004PhRvD..70l5012A }}</ref><ref name="Aloisio2005">
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| {{Cite journal
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| |first=R. |last=Aloisio |first2=A. |last2=Galante |first3=A.F. |last3=Grillo
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| |first4=E. |last4=Luzio |first5=F. |last5=Mendez
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| |title=A note on DSR-like approach to space–time
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| |journal=[[Physics Letters B]]
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| |volume=610 |issue= |pages=101–106
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| |year=2005
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| |arxiv=gr-qc/0501079
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| |doi=10.1016/j.physletb.2005.01.090
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| |bibcode = 2005PhLB..610..101A }}</ref> Most notably it is difficult to recover the standard transformation behavior for macroscopic bodies, known as the soccer-ball-problem. The other conceptual difficulty is that DSR is ''a priori'' formulated in momentum space. There is as yet no consistent formulation of the model in position space.
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| There are many other Lorentz violating models in which, contrary to DSR, the [[principle of relativity]] and Lorentz invariance is violated by introducing [[preferred frame]] effects. Examples are the [[effective field theory]] of [[Sidney Coleman]] and [[Sheldon Lee Glashow]], and especially the [[Standard-Model Extension]] which provides a general framework for Lorentz violations. These models are capable of giving precise predictions in order to assess possible Lorentz violation, and thus are widely used in analyzing experiments concerning the standard model and special relativity (see [[Modern searches for Lorentz violation]]).
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| ==Main==
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| In principle, it seems difficult to incorporate an invariant length magnitude in a theory which preserves Lorentz invariance due to Lorentz–FitzGerald contraction, but in the same way that special relativity incorporates an invariant velocity by modifying the high-velocity behavior of [[Galilean transformations]], DSR modifies Lorentz transformations at small distances (large energies) in such a way to admit a length invariant scale without destroying the principle of relativity. The postulates on which DSR theories are constructed are:
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| # The principle of relativity holds, i.e. equivalence of all inertial observers.
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| # There are two observer-independent scales: the speed of light, c, and a length (energy) scale <math>\lambda</math> (<math>\eta=1/\lambda</math>) in such a way that when λ → 0 (η → ∞), special relativity is recovered.
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| As noted by Jerzy Kowalski-Glikman, an immediate consequence of these postulates is that the symmetry group of DSR theories must be ten dimensional, corresponding to ''boosts'', rotations and translations in 4 dimensions. Translations, however, cannot be the usual Poincaré generators as it would be in contradiction with postulate 2). As translation operators are expected to be modified, the usual [[dispersion relation]]
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| :<math>E^2-p^2=m^2</math>
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| is expected to be modified and, indeed, the presence of an energy scale, namely <math>\eta</math>, allows introducing <math>\eta</math>-suppressed terms of higher order in the dispersion relation. These higher momenta powers in the dispersion relation can be traced back as having their origin in higher dimensional (i.e. non-renormalizable) terms in the Lagrangian.
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| It was soon realized that by deforming the Poincaré (i.e. translation) sector of the Poincaré algebra, consistent DSR theories can be constructed. In accordance with postulate 1), the Lorentz sector of the algebra is not modified, but just non-linearly realized in their action on momenta coordinates. More precisely, the Lorentz Algebra
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| :<math>[M_i,M_j]=i\epsilon_{ijk} M_k </math>
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| :<math>[N_i,N_j]=-i\epsilon_{ijk} M_k,</math>
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| :<math> [M_i,N_j]=-i\epsilon_{ijk} N_k</math>
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| :<math>[M_i,p_j]=i\epsilon_{ijk} p_k</math>
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| :<math>[M_i,p_0]=0</math>
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| remains unmodified, while the most general modification on its action on momenta is
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| :<math>[N_i,p_j]=A\epsilon_{ij}+Bp_ip_j+C\Delta^\epsilon_{ijk}N_k</math>
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| :<math>[N_i,p_0]=Dp_i</math>
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| where A, B, C and D are arbitrary functions of <math>{p_i, p_0,\eta}</math> and M,N are the rotation generators and boost generators, respectively. It can be shown that C must be zero and in order to satisfy the Jacobi identity, A, B and D must satisfy a non-linear first order differential equation. It was also shown by Kowalski-Glikman that these constraints are automatically satisfied by requiring that the boost and rotation generators N and M, act as usual on some coordinates <math>\eta_A
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| </math> (A=0,...,4) that satisfy | |
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| :<math>-\eta^2=\eta_0^2-\eta_1^2-\eta_2^2-\eta_3^2-\eta_4^2</math>
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| i.e. that belong to [[de Sitter space]]. The physical momenta <math>p_\mu</math> are identified as coordinates in this space, i.e.
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| :<math>p_\mu=p_\mu(\eta_A,\eta)</math>
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| and the [[dispersion relation]] that these momenta satisfy is given by the invariant
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| :<math>m^2=\eta_0^2(p_\mu,\eta)-\eta_i^2(p_\mu,\eta)</math>.
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| This way, different choices for the "physical momenta coordinates" in this space give rise to different modified [[dispersion relations]], a corresponding modified [[Poincaré algebra]] in the Poincaré sector and a preserved underlying [[Lorentz invariance]].
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| One of the most common examples is the so-called Magueijo–Smolin basis (Also known as the DSR2 model), in which:
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| :<math>\eta_\mu=\frac{p_\mu}{1-P_0/\eta}</math>
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| which implies, for instance,
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| :<math>[N_i,P_0]=iP_i\left(1-\frac{P_0}{\eta}\right)</math>,
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| showing explicitly the existence of the invariant energy scale <math>P_0=\eta</math> as <math>[N_i,P_0=\eta]=0</math>.
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| The theory was highly speculative as of first publishing in 2002, as it relies on no experimental evidence so far. It would be fair to say that DSR is not considered a promising approach by a majority of members of the [[high-energy physics]] community, as it lacks experimental evidence and there's so far no guiding principle in the choice for the particular DSR model (i.e. basis in momenta de Sitter space) that should be realized in nature, if any.
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| DSR is based upon a generalization of symmetry to [[quantum group]]s. The [[Poincaré symmetry]] of ordinary [[special relativity]] is deformed into some [[noncommutative]] [[symmetry]] and [[Minkowski space]] is deformed into some [[noncommutative space]]. As explained before, this theory is not a violation of Poincaré symmetry as much as a deformation of it and there is an exact de Sitter symmetry. This deformation is scale dependent in the sense that the deformation is huge at the Planck scale but negligible at much larger length scales. It's been argued that models which are significantly Lorentz violating at the Planck scale are also significantly Lorentz violating in the infrared limit because of radiative corrections, unless a highly unnatural fine-tuning mechanism is implemented. Without any exact Lorentz symmetry to protect them, such Lorentz violating terms will be generated with abandon by quantum corrections. However, DSR models do not succumb to this difficulty since the deformed symmetry is exact and will protect the theory from unwanted radiative corrections — assuming the absence of [[quantum anomalies]]. Furthermore, models where a privileged rest frame exists can escape this difficulty due to other mechanisms.
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| Jafari and Shariati have constructed [[canonical transformation]]s that relate both the doubly special relativity theories of Amelino-Camelia and of Magueijo and Smolin to ordinary special relativity. They claim that doubly special relativity is therefore only a complicated set of coordinates for an old and simple theory. However, the momentum space in deformed special relativity is curved, which is a statement independent of the choice of coordinates. The argument that deformed special relativity is equivalent to special relativity resurfaces on occasion but is widely known to be wrong. The error in the argument comes about because they are based on an incomplete specification of the structure of [[phase-space]].
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| ==Predictions==
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| Experiments to date have not observed contradictions to special relativity (see [[Modern searches for Lorentz violation]]).
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| It was initially speculated that ordinary special relativity and doubly special relativity would make distinct physical predictions in high energy processes, and in particular the derivation of the [[Greisen–Zatsepin–Kuzmin limit]] would not be valid. However, it is now established that standard doubly special relativity does not predict any suppression of the GZK cutoff, contrary to the models where an [[preferred frame|absolute local rest frame]] exists, such as [[effective field theory|effective field theories]] like the [[Standard-Model Extension]].
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| Since DSR generically (though not necessarily) implies an energy-dependence of the speed of light, it has further been predicted that, if there are modifications to first order in energy over the Planck mass, this energy-dependence would be observable in high energetic [[photon]]s reaching Earth from distant [[gamma ray burst]]s. Depending on whether the now energy-dependent speed of light increases or decreases with energy (a model-dependent feature) highly energetic photons would be faster or slower than the lower energetic ones
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| .<ref name="Smolin2009">
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| {{Cite journal
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| |first=G. |last=Amelino-Camelia |first2=L. |last2=Smolin
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| |title=Prospects for constraining quantum gravity dispersion with near term observations
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| |journal=[[Physical Review D]]
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| |volume=80 |issue= |pages=084017
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| |year=2009
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| |arxiv=0906.3731
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| |doi=10.1103/PhysRevD.80.084017
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| |bibcode = 2009PhRvD..80h4017A }}</ref>
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| However, the [[Fermi Gamma-ray Space Telescope|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.<ref name=lat>{{cite journal |author=Fermi LAT Collaboration|title=A limit on the variation of the speed of light arising from quantum gravity effects|journal=Nature|volume=462|issue=7271 |year=2009|pages=331–334|doi=10.1038/nature08574|arxiv=0908.1832|pmid=19865083
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| |bibcode = 2009Natur.462..331A }}</ref>
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| It has moreover 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.<ref name="Hossenfelder2009">
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| {{cite arxiv
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| |first=S. |last=Hossenfelder
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| |title=The Box-Problem in Deformed Special Relativity
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| |year=2009
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| |eprint=0912.0090
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| |bibcode = 2009arXiv0912.0090H }}</ref>
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| ==de Sitter relativity==
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| {{Main|de Sitter relativity}}
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| Since the de Sitter group naturally incorporates an invariant length–parameter, de Sitter relativity can be interpreted as an example of doubly special relativity. 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.
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| ==In-line notes and references==
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| {{Reflist}}
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| ==See also==
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| * [[Scale relativity]]
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| * [[Planck scale]]
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| * [[Planck units]]
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| * [[Planck epoch]]
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| * [[Fock–Lorentz symmetry]]
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| ==Further reading==
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| *{{Cite journal
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| |last=Amelino-Camelia |first=G.
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| |title=Doubly-Special Relativity: First Results and Key Open Problems
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| |journal=[[International Journal of Modern Physics D]]
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| |volume=11 |issue=10 |pages=1643–1669
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| |year=2002
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| |doi=10.1142/S021827180200302X
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| |arxiv = gr-qc/0210063 |bibcode = 2002IJMPD..11.1643A }}
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| *{{Cite journal
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| |last=Amelino-Camelia |first=G.
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| |title=Relativity: Special treatment
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| |journal=[[Nature (journal)|Nature]]
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| |volume=418 |issue=6893 |pages=34–35
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| |year=2002
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| |doi=10.1038/418034a
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| |pmid=12097897
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| |arxiv = gr-qc/0207049 |bibcode = 2002Natur.418...34A }}
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| *{{Cite book
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| |last=Cardone |first=F. |authorlink=Fabio Cardone
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| |coauthors=Mignani, R.
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| |title=Energy and Geometry: An Introduction to Deformed Special Relativity
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| |year=2004
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| |publisher=[[World Scientific]]
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| |isbn=981-238-728-5
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| }}
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| *{{Cite conference
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| |last=Jafari |first=N.
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| |coauthors=Shariati, A.
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| |year=2006
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| |title=Doubly Special Relativity: A New Relativity or Not?
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| |booktitle=AIP Conference Proceedings
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| |volume=841 |issue= |pages=462–465
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| |arxiv=gr-qc/0602075 |doi=10.1063/1.2218214
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| }}
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| *{{Cite book
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| |last=Kowalski-Glikman |first=J.
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| |chapter=Introduction to Doubly Special Relativity
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| |title=Planck Scale Effects in Astrophysics and Cosmology
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| |series=Lecture Notes in Physics
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| |volume=669 |pages=131–159
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| |year=2005
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| |publisher=[[Springer Science+Business Media|Springer]]
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| |isbn=978-3-540-25263-4
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| |arxiv=hep-th/0405273 |doi=10.1007/b105189
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| }}
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| *{{Cite book|title=The trouble with physics : the rise of string theory, the fall of a science, and what comes next
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| |last=[[Lee Smolin|Smolin, Lee.]]
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| |year=2006 |publisher=Houghton Mifflin |location=Boston, MA
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| |isbn=978-0-618-55105-7 |oclc=64453453
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| |chapter= Chapter 14. Building on Einstein
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| |accessdate=19 August 2010}} 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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| ==External links==
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| *[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=205100 Doubly-special relativity on arxiv.org]
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| {{DEFAULTSORT:Doubly Special Relativity}}
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| [[Category:Special relativity]]
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