a r
X
i
v
:g r
-
q
中国机长观后感c
家常白菜/
2
7
4
9
v 1
1
2
J u
相思病是啥意思l
2
精华英语2
gr-qc/0207049preprint version 1of Nature 418(2002)34-35Doubly Special Relativity Giovanni AMELINO-CAMELIA Dipartimento di Fisica,Universit`a “La Sapienza”,P.le Moro 2,I-00185Roma,Italy ABSTRACT I give a short non-technical review of the results obtained in recent work on “Doubly Spe
cial Relativity”,the relativistic theories in which the rota-tion/boost transformations between inertial obrvers are characterized by two obrver-independent scales (the familiar velocity scale,c ,and a new obrver-independent length/momentum scale,naturally identified with the Planck length/momentum).I emphasize the aspects relevant for the arch of a solution to the cosmic-ray paradox.Galilei/Newton Relativity was abandoned becau of the conflicting results of the
Michelson-Morley experiments and becau of its incompatibility with the mathemati-cal structure of the successful Maxwell theory of electromagnetism.After a century of success,Einstein’s Special Relativity,the theory that replaced Galilei/Newton Rela-tivity,could
now be questioned for similar reasons.A key Special-Relativity prediction appears to be violated by certain obrvations of ultra-high-energy cosmic rays [1],and
some Quantum-Gravity
arguments appear to encourage a modification of Special Rel-ativity.I argued in Ref.[2]that this situation can provide motivation for considering
a change in the Relativity postulates somewhat analogous to the one needed for the transition from
Galilei/Newton Relativity to Einstein’s Relativity:the introduction of a new absolute obrver-independent scale.I analyzed in detail a first illustrative ex-
ample of relativity postulates with an obrver-independent length(momentum)scale,in addition to the familiar obrver-independent velocity scale c ,and I showed that there is no in principle obstruction for the construction of such new relativistic theo-ries.That illustrative example of new relativistic theory also predicts some new effects of a type that could explain
the
obrvations
of
ultra-high-energy cosmic rays,but the
predicted magnitude of the effects turns out to be too weak for a description of the
data.For nearly a year,follow-up studies [3]focud on the example of new relativistic
theory which I had ud to illustrate the idea.In a very recent paper[4],Maguejio and Smolin constructed a cond example of relativistic theory of the type propod in Ref.[2],and this has generated incread interest[5,6,7,8,9,10,11]in rearch on relativity theories with two obrver-independent scales.The theories are being called2“Doubly Special Relativity”(DSR)theories.Some of the key open issues that are being studies concern the arch of other examples of DSR theories,the study of the multi-particle ctor of given DSR theories,and attempts offinding a full solution of the cosmic-ray paradox within DSR.
An aspect of cosmic-ray obrvations that is directly connected with relativity is the Grein-Zatpin-Kuzmin(GZK)limit.Ultra-high-energy cosmic rays are parti-cles,most likely protons,produced by distant active galaxies,which we detect through the particle-physics process they ignite in the atmosphere.The GZK limit is related with the threshold energy,E GZK,required for such cosmic rays to interact with the “Cosmic Microwave Background Radiation”(CMBR):becau of the interactions with the CMBR it should not be possible for cosmic rays with energies above E GZK to reach us.The value of the threshold energy E GZK is a purely kinematical prediction. In a given relativity theory it is obtained by combining the laws of energy-momentum conrvation and the dispersion relation(the relation between the energy and the mo-mentum of a particle).Within Spe
四十岁的女人cial Relativity onefinds E GZK≃5·1019eV,but veral cosmic-ray events[1]are in disagreement with this prediction.As with all emerging experimental paradoxes it is of cour possible that the cosmic-ray paradox is the result of an incorrect analysis of the experiment,for example it is legitimate to speculate that the identification of the ultra-high-energy cosmic rays as protons produced by distant active galaxies might eventually turn out to be incorrect.But,in spite of its preliminary status,this cosmic-ray paradox provides encouragement for the study of new relativity postulates.
Besides this motivation coming for the experimental side,the idea of revising the relativity postulates alsofinds encouragement becau of the role that the“Planck scale”E p≃1028eV plays in certain Quantum-Gravity scenarios.Various arguments lead to the expectation that for particles with energies clo to E p it would be necessary to describe spacetime in terms of one form or another of new spacetime quanta,while for our readily available particles with energies much smaller than E p the familiar
classical-spacetime picture would remain valid.It would be appealing to introduce such a transition scale,a scale at which our description of physical phenomena changes significantly,as an obrver-independent kinematical scale.
Just like in going from Galilei/Newton Relativity to Einstein’s Special Relativity a key role is played by the law of composition of velocities,which for Einstein must reflect the special status of the speed-of-light constant c,in going then from Special Relativity to DSR a key role is played by the law of composition of energy-momentum,which, in the new framework,must attribute a special status to the Planck scale E p.This modification of the laws of energy-momentum conrvation also affects the evaluation of the mentioned threshold energy E GZK that is relevant for the cosmic-ray paradox. Indeed the DSR theory which I considered as illustrative example in Ref.[2]predicts, besides the emergence of a maximum momentum of order E p for fundamental particles, a deformation of the laws of energy-momentum conrvation.In turn the deformed laws of energy-momentum conrvation of the DSR theory of Ref.[2]leads to a value of E GZK which is different from the one predicted by ordinary Special Relativity,but the difference is not as large as required for a full explanation of the cosmic-ray paradox. The DSR theory more recently propod[4]by Maguejio and Smolin predicts that E p ts the maximum value of both energy and momentum for fundamental particles.The corresponding deformation[5]of the laws of energy-momentum conrvation leads to yet another alternative prediction for E GZK,but that too is not sufficient to solve the cosmic-ray paradox.
A lot has been understood of the DSR theories,but veral issues must still be investigated.At prent,since the status of the paradox is still preliminary,the arch of a solution to the cosmic-ray paradox is not to be en as a consistency condition for the DSR rearch programme,but the emergence of a compelling phenomenological result would legitimate interest in the rather speculative DSR idea.The recent study[4] by Magueijo and Smolin,by showing that there exist more than one example of DSR theories,provides indirect encouragement for the arch of a DSR theory that would solve the cosmic-ray paradox.It appears[2,5,12]that a DSR theory capable of solving the cosmic-ray paradox should rely on the introduction of some structure not yet prent in the DSR theories discusd in Refs.[2]and[4].This new structure should enter the law of composition of energy-momentum,which,through energy-momentum conrvation,affects the evaluation of E GZK.
烤牛排Interestingly,the law of composition of energy-momentum also plays a role in an-other open problem for DSR theories:while Planck-scale deformed dispersion relations, generically predicted in DSR[2,4],are fully consistent with our obrvations of funda-mental/microscopic particles,they are clearly in conflict with obrvations of macro-scopic bodies.Therefore the rule that defines the total momentum of a macroscopic body in terms of the momenta of the composing microscopic particles must allow the emergence of different relativistic properties for macroscopic and microscopic entities3. Such a difference between macroscopic and microscopic entities could not be accom-
modated in ordinary Special Relativity,but,remarkably,through the prence of an obrver-independent energy/momentum scale,DSR naturally provides room[2,12] for a macro/micro paration.Unfortunately,it is still unclear in which specific way this macro/micro paration would be best implemented.In particular,it is unclear whether or not we should assume that the total energy-momentum of a multi-particle system is constructed in terms of the energy-momentum of each composing particle ac-cording to laws that are themlf obrver-independent laws.In addition to the already difficult task of describing a system of free particles both in terms of the momenta of each particle and in terms of the total momentum of the system,even more conceptually challenging for DSR theories is the description of the relativistic properties of bound states(macroscopic particles which are in a n compod of veral fundamental particles,but the composing particles are not free).Besides the indirect connection with the cosmic-ray paradox through the laws of composition of energy-momentum, this issue of the macro/micro paration could turn out to be even directly relevant for the analysis of the cosmic-ray paradox if it is established that(some of)the relevant particles(protons,pions,photons)must be described as composite objects in DSR.
The role of certainκ-Poincar´e Hopf algebras[13]in DSR theories is also a lively subject of investigation[2,6,7,12].In the one-particle ctor of the DSR theories so far considered the Lorentz s
ector of certainκ-Poincar´e Hopf algebras plays a role that is analogous4to the role of the Lorentz algebra in Einstein’s Special Relativity: the operators of the(Hopf)algebra are ud to describe infinitesimal rotation/boost transformations between inertial obrvers.But for what concerns the delicate issues just mentioned above,the ones that involve the two-particle and multi-particle c-tors,the role ofκ-Poincar´e Hopf algebras remains unclear[2,12].It would also be interesting to establish whether it is possible to construct DSR theories without any u ofκ-Poincar´e Hopf algebras,not even for the infinitesimal transformations of the one-particle ctor.In fact,the DSR proposal[2]just requires that the laws of rota-tion/boost transformation between inertial obrvers have a lenght(momentum)and a velocity obrver-independent scales,and it might be possible to realize this proposal in a variety of mathematical frameworks.
The debate on the open issues is likely to keep busy the interested scientists for the next few years.Experimental help could come soon from improved data on the mentioned ultra-high-energy cosmic rays;moreover,in2006,when related stud-ies[14]will be performed on the GLAST space telescope,we should have conclusive information on another key prediction of some DSR theories:a possible wavelength dependence[2,12]of the speed of photons.
References
[1]D.J.Bird et al.,Astrophys.J.441(1995)144[arXiv:astro-ph/9410067].
[2]G.Amelino-Camelia,Int.J.Mod.Phys.D11(2002)35[arXiv:gr-qc/0012051];
Phys.Lett.B510(2001)255[arXiv:hep-th/0012238].
[3]S.Alexander and J.Magueijo,hep-th/0104093;N.R.Bruno,G.Amelino-Camelia
and J.Kowalski-Glikman,Phys.Lett.B522(2001)133;J.Kowalski-Glikman Mod.Phys.Lett.A17(2002)1;S.Liberati,S.Sonego and M.Visr Annals Phys.298(2002)167.
[4]J.Magueijo and L.Smolin,Phys.Rev.Lett.88(2002)190403.
[5]G.Amelino-Camelia,D.Benedetti,F.D’Andrea,hep-th/0201245.
ugears[6]J.Kowalski-Glikman and S.Nowak,hep-th/0203040.
[7]J.Lukierski and A.Nowicki,hep-th/0203065.
老公英语怎么写[8]S.Judes,and M.Visr,gr-qc/0205067.
[9]D.V.Ahluwalia and M.Kirchbach,gr-qc/0207004.
[10]J.Rembielinski and K.A.Smolinski,hep-th/0207031.
[11]A.Granik,hep-th/0207113.
[12]G.Amelino-Camelia,gr-qc/0106004(in“Karpacz2001,New developments in fun-
damental interaction theories”pag.137-150).
[13]J.Lukierski,A.Nowicki,H.Ruegg,and V.N.Tolstoy,Phys.Lett.B264(1991)
331;S.Majid and H.Ruegg,Phys.Lett.B334(1994)348;J.Lukierski,H.Ruegg and W.J.Zakrzewski Ann.Phys.243(1995)90.
[14]G.Amelino-Camelia,J.Ellis,N.E.Mavromatos,D.V.Nanopoulos and S.Sarkar,
Nature393(1998)763.
5
