百度相对论吧手册兼资源导航 20110113 Alpha版

合集下载

相对论ppt课件

星体
宇宙中很可能存在黑洞，它
不辐射电磁波，因此无法直接观测，但是它的巨大质量和极小的体积使其附近产生极强的引力场，引力透镜是探索黑洞的途径之一．
无
法
黑
星体
观
洞
测
32
时间间隔与引力场有关
引力场的存在使得空间不同位置的时间进程出现差别．
对于高速转动的圆盘，除了转动轴的位置外，各点都在做加速运动，越是靠近边缘，加速度越大，方向指向盘心．
3、时间和空间相互独立、互不相关。
4
相对论简黑介体辐两射朵乌云
光速问
19世纪后半叶，关于电磁场的研究不题断深入，
人们认识到了光的电磁本质．我们已经知道，电
磁波是以巨大且有限的速度传播的，因此在电磁
场的研究中不断遇到一些矛盾，这些矛盾导致了
相对论的出现．
量子力学
相对论
相对论不仅给出了物体在高速运动时所遵循的规
15
狭义相对论的其他三个结论下面，我们学习狭义相对论的三个重要结论…
相对论的速度叠加公式相对论质量质能方程
16
相对论的速度叠加公式
v
u
车外的人看到车上人
相对地面的速度为：
u v
u

1
uv c2
17
相对论质量
物体的运动速度不能无限增加，那么物体的质量是否随着速度而变化？
严格的论证表明，物体高速（与光速相比）运动时的质量与它静止时的质量之间有下面的关系：
地面上看到：越是靠近边缘，速度越大．根据狭义相对论，靠近边缘部位的时间进程较慢．
圆盘上的人认为：盘上存在引力场，方向由盘心指向边缘，引力势较低，得出：引力势较低的位置，时间进程比较慢． 33

Vorton Formation

a rXiv:h ep-ph/984378v123Apr1998Vorton FormationC.J.A.P.Martins ∗and E.P.S.Shellard †Department of Applied Mathematics and Theoretical Physics University of Cambridge Silver Street,Cambridge CB39EW,U.K.In this paper we present the ﬁrst analytic model for vorton forma-tion.We start by deriving the microscopic string equations of motion in Witten’s superconducting model,and show that in the relevant chiral limit these coincide with the ones obtained from the supersonic elastic models of Carter and Peter.We then numerically study a number of solutions of these equations of motion and thereby suggest criteria for deciding whether a given superconducting loop conﬁguration can form a vorton.Finally,using a recently developed model for the evolution of currents in superconducting strings we conjecture,by comparison with these criteria,that string networks formed at the GUT phase transition should produce no vortons.On the other hand,a network formed at the electroweak scale can produce vortons accounting for up to 6%of the critical density.Some consequences of our results are discussed.I.INTRODUCTION As ﬁrst pointed out by Witten [1],cosmic strings can in some circumstances (typically when the electromagnetic gauge invariance is broken inside the string)behave as ‘superconducting wires’carrying large currents and charges—up to the order of the string mass scale in appropriate units.The charge carriers can be either bosons or fermions (see [2]for a review).The former type occurs when it becomes energetically favourable for a charged Higgs ﬁeld to have a non-zero vacuum expectation value in the string core;the latter happens when fermions couple to the string ﬁelds creating fermion zero modes.It is well known that arbitrarily large currents are not allowed—there is a criticalvalue beyond which the current saturates.In other words,for large enough wind-ing number per unit length,the superconducting condensate is quenched down,suppressing the current ﬂow.Also,the current can decay by magnetic ﬂux-line tun-nelling;this can be used to impose constraints on allowed particle physics models.If superconducting strings carry currents,they must also carry charges of similar magnitude.This includes not only charges trapped at formation by the Kibble mechanism but also the ones due to string inter-commuting between regions of the string network with diﬀerent currents.Just like with currents,charge densities cannot have arbitrarily large magnitude—there is a limit beyond which there will no longer be an energy barrier preventing the charge carriers from leaving the string.A rather important point is that the presence of charges on the string tends to counteract the current quenching eﬀect discussed above.In fact,numerical simula-tions of contracting string loops at ﬁxed charge and winding number have shown [3]that a‘chiral’state with equal charge and current densities is approached as the loop contracts.In this limiting chiral case,quenching is in fact eliminated completely. This has several important consequences.Strings that have trapped charges as a consequence of a phase transition can become superconducting even if the formation of a condensate was otherwise energetically unfavoured.More importantly,a string with both a charge and a current density will have a non-zero angular momentum. In the cosmological context,these strings would of course interact with the cosmic plasma,originating a number of interesting consequences.The most remarkable of these,however,has to do with the evolution of string loops.If a superconducting string loop has an angular momentum,it is semi-classically conserved,and it tries to resist the loop’s tension.This will at least increase the loop’s lifetime.If the current is too large,charge carriers will leave the string accompanied by a burst of electromagnetic radiation,but otherwise it is possible that dynamically stable loops form.These are called vortons[4]—they are stationary rings that do not ra-diate classically,and at large distances they look like point particles with quantised charge and angular momentum.Their cosmological signiﬁcance comes from the fact that they provide very strong constraints on allowed particle physics models, since they behave like non-relativistic particles.According to current belief[4,5], if they are formed at high enough energy scales they are as dangerous as magnetic monopoles,producing an over-density of matter in disagreement with observations. On the other hand,low-mass vortons could be a very interesting dark matter can-didate.Understanding the mechanisms behind formation and evolution is therefore an essential cosmological task.The overwhelming majority of the work done on cosmic strings so far was con-cerned with the structureless Goto-Nambu strings(but see[6]and references therein for some exceptions).In the case of work on vortons,this means that somewhat ad-hoc estimates had to be made for some properties of the cosmic string network—notably for microscopic quantities such as current and charge densities.This is de-spite the fact it has been recognised a long time ago that,even though they might be computationally very useful[7–9],Goto-Nambu models cannot realistically be expected to account for a number of cosmologically relevant phenomena,due to the very limited number of degrees of freedom available.Two such phenomena are the build-up of small-scale structure and charge and current densities.In this paper weﬁll this important gap by discussing the problem of vorton formation in the context of the superconducting string models of Witten[1]and of Carter and Peter[10](sections II and III).Strangely enough,the issue of the conditions for vorton formation has been so far neglected with respect to those of their stability and cosmological consequences.We will start by introducing these models and determining the microscopic string equations of motion in each case.It will be shown that in the relevant chiral limit these equations coincide—this also provides theﬁrst conclusive evidence of the validity of the supersonic elastic models of Carter and Peter[10].We then proceed to study the evolution of a number of loop solutions of these equations numerically(sections IV and V),and from the results of this analysis parameters will be introduced which characterise the loop’s ability to evolve into a vorton state(section VI).Finally,we discuss a very simple phenomenological model for the evolution of the superconducting currents on the long cosmic string network [11],based on the dynamics of a‘superconducting correlation length’(sections VII–VIII).Using this model we can therefore estimate the currents carried by string loops formed at all relevant times,and thus(in principle)decide if these can become vortons(section IX)and calculate the corresponding density(section X).Based on our results,we don’t expect any GUT vortons to form at all.This is essentially because the friction-dominated epoch is very short for GUT-scale strings [7],so their currents and charges are never large enough to prevent them frombecoming relativistic—and therefore liable to losses.Even if they did form,they wouldn’t be in conﬂict with the standard cosmological scenario if they decayed soon after the end of the friction-domination epoch.Hence we conclude that,in contrast with previously existing estimates[4,5], one cannot at the moment rule out GUT superconducting string models.We should point out at the outset that there are essentially three improvements in the present work which justify the diﬀerent end result for GUT-scale strings.Firstly,by analysing simple(but physically relevant)loop solutions of the microscopic string equations of motion for the Witten model,we can get a much improved idea of how superconducting loops evolve and of how(and under which conditions)they reach a vorton state.Secondly,by using a simple model for the evolution of the currents on the long strings[11]we can accurately determine the typical currents on each string loop at the epoch of its formation.Finally,the use of the analytic formalism previously introduced by the present authors[7,9]allows us to use a quantitative description throughout the paper,and in particular to determine the loop sizes at formation.As will become clear below,when taken together these allow a detailed analysis of the process of vorton formation to be carried out,either in the Witten model(as is done in this paper)or any other that one considers relevant.In contrast,note that Davis&Shellard[4]restrict themselves to the particular case of the initial Brownian Vachaspati-Vilenkin loops with Kibble currents,and do not consider the subsequent evolution of the network.On the other hand,Brandenberger et al.[5] make rather optimistic order-of-magnitude estimates about the process of relaxation into a vorton state.As it turns out,for high energy GUT scales,all these loops be-come relativistic before reaching a vorton state.Finally,neither of these treatments has the beneﬁt of a quantitative model for the evolution of the long-string network [7]which allows one to accurately describe the process of loop production.On the other hand,as we lower the string-forming energy scale we expect more and more eﬃcient vorton production,and the’old’scenario still holds.Therefore intermediate-scale superconducting strings are still ruled out,since they would lead to a universe becoming matter-dominated earlier than observationally allowed.Fi-nally,at low enough energy scales,vortons will be a dark matter candidate.For example,for a string network formed around T∼102GeV(typical of the elec-troweak phase transition)they can provide up to6%of the critical density.A more detailed discussion of these issues is left to a forthcoming publication[12]. Throughout this paper we will use fundamental units in which¯h=c=k B= Gm2P l=1.II.WITTEN’S MICROSCOPIC MODELAsﬁrst pointed out by Witten[1],a low-energy eﬀective action for a supercon-ducting string can be derived in a way that is fairly similar to what is done in the Goto-Nambu case(see for example[2]).One has to adopt the additional as-sumptions that the current is much smaller than the critical current and that the electromagnetic vector potential Aµis slowly varying on the scale of the condensate thickness.The derivation then proceeds as in the neutral case,except for the use of the well-known fact that in two dimensions a conserved current can be written as the derivative of a scalarﬁeld.One obtainsS= √2γabφ,aφ,b−qAµxµ,aǫab−γφ,b d2σ(2.1)−1−gFµνFµν;(2.2) the four terms are respectively the usual Goto-Nambu term,the inertia of the charge carriers,the current coupling to the electromagnetic potential and the external electromagneticﬁeld(ǫab is the alternating tensor);note that this applies to both the bosonic and the fermionic case[2].Recalling the usual deﬁnitionsA a=xµ,a Aµ,(2.3)F ab=Fµνxµ,a xν,b=A b,a−A a,b,(2.4) and deﬁningΥab to be the stress-energy tensor of the scalarﬁeldφΥab=φ,aφ,b−1√−γγabφ,b +1−γ˜ǫab F ab=0,(2.8) and∂a √µ0Υab xα,b +√µ0Υab Γασρxσ,a xρ,b=(2.9)√=gαλ(gαµ,ν+gνα,µ−gµν,α),(2.11)2and Fαis the Lorentz force1Fα=ℓf uα−xα,a xσ,a uσ ,(2.13) using the same procedure as described in[13,7].As shown in[11],plasma eﬀects are subdominant,except possibly in the presence of background magneticﬁelds—either of‘primordial’origin or generated(typically by a dynamo mechanism)onceproto-galaxies have formed.Hence one expectsAharonov-Bohm scattering [14]to be the dominant eﬀect,and consequently we have [7]ℓf =µµ0γ00,(2.17)and choosing the standard gauge conditionsσ0=τ,˙x ·x ′=0,(2.18)(with dots and primes respectively denoting derivatives with respect to the time-like and space-like coordinates on the worldsheet as usual)the string equations of motion in an FRW background with the line element ds 2=a 2 dτ2−dx 2 (2.19)(which implies that γ00=a 2(1−˙x 2))have the form[ǫ(1+Φ)]˙+ǫa ǫΦ,(2.20)andǫ(1+Φ)¨x +ǫǫ ′+ ˙Φ+2˙a ℓd =a 2H +1ǫ.(2.24)Note that the Witten action is ‘microscopic’in the sense of being built using only the properties of the underlying particle physics model [1].In the next section we will analyse the equations of motion obtained form the action for the elastic supersonic models of Carter and Peter [10],which is is this sense ‘macroscopic’.III.SUPERSONIC ELASTIC MODELSIn order to account for phenomena such as the build-up of charge and current densities on cosmic strings,one must introduce additional degrees of freedom on the string worldsheet.One such class of models,originally introduced by Carter and co-workers is usually referred to as elastic models(see[6]and references therein,on which the following two subsections are based).A.Basics of elastic modelsIn general,elastic string models can be described by a Lagrangian density de-pending on the spacetime metric gµν,backgroundﬁelds such as a Maxwellian-type gauge potential Aµor a Kalb-Ramond gaugeﬁeld Bµν(but not their gradients) and any relevant internalﬁelds(that will be discussed in detail below).Note that the Goto-Nambu model has a constant Lagrangian density,namelyL GN=−µ0.(3.1) Upon inﬁnitesimal variations in the backgroundﬁelds,and provided that indepen-dent internalﬁelds are keptﬁxed(or alternatively that their dynamic equations of motion are satisﬁed),the action will change byδS=−1−γd2σ,(3.2)whereTµν=2δLδAµ(3.4) is the worldsheet electromagnetic current density,andWµν=2δLNote that U and T are simply constants for a Goto-Nambu string,U=T=µ0,(3.8) but they are variable in general—hence the name‘elastic strings’.In particular, one should expect that the string tension in an elastic model will be reduced with respect to the Goto-Nambu case due to the mechanical eﬀect of the current. Since elastic string models necessarily possess conserved currents,it is convenient to deﬁne a‘stream function’ψon the worldsheet that will be constant along the current’sﬂow lines.The part of the Lagrangian density L containing the internal ﬁelds is usually called the‘master function’,and can be deﬁned as a function of the magnitude of the gradient of this stream function,Λ=Λ(χ),such thatχ=γabψ;aψ;b,(3.9) where the gauge covariant derivative is deﬁned asψ;a=∂aψ−eAµxµ,a.(3.10) Note that the deﬁnition ofχdiﬀers by a minus sign from that of Carter[6];the reason for this will become clear below.This‘dynamic’term contains charge cou-plings,whose relevance will be further discussed below.Nevertheless,whether or not these or other background gaugeﬁelds are present,it is always the form of the master function which determines the equation—or equations—of state.There is also a dual[15]potential˜ψ,whose gradient is orthogonal to that ofψ, and the corresponding dual master function˜Λ=˜Λ(˜χ)such that˜χ=γab˜ψ;a˜ψ;b,(3.11) with the obvious deﬁnition for˜ψ;a.The duality between these descriptions means that theﬁeld equations for the stream functionψobtained with the master function Λare the same as those for the dual potential˜ψobtained with the dual master function˜Λ.However,there will in general be two diﬀerent equation of state relating the energy density U and the tension T;these correspond to what is known as the ‘magnetic’and‘electric’regimes,respectively corresponding to the cases˜χmg<0<χmg(3.12) andχel<0<˜χel,(3.13) that are respectively characterised by space-like and time-like currents.In the degenerate null state limit,however,there will be a single equation,U=T=µ0.(3.14) Note that the distinction between a given model and its dual disappears in the absence of charge couplings;such models are then called‘self-dual’for obvious reasons.In each case the equation of state provides the expressionsc2E=TdU =νdν,(3.16)for the extrinsic(that is transverse,or‘wiggle’)and for the sound-type(longitudinal or‘woggle’)perturbations of the worldsheet.Both of these must obey c2≥0(a requirement for local stability)and c2≤1(a requirement for local causality).These two speeds can be used to characterise the elastic model in question;in particular there is a straightforward but quite meaningful division of the models into supersonic (that is,those obeying c E>c L),transonic(c E=c L;only in the null limit is this common speed unity)and subsonic(c E<c L).B.Supersonic(superconducting)modelsCarter and Peter[10]have recently proposed two supersonic elastic models to describe the behaviour of current-carrying cosmic strings.The Lagrangian density in the magnetic regime is˜Λmg =−m2+˜χ2k0m2σ −1,(3.17)mσbeing the current carrier mass(which is at most of the order of the relevant Higgs mass);this is valid in the range−1k0m2σ<1−k0m2σm2=1+k0m2σk02mσm2−1+k0m2σ2ln 1−˜χk0m2σ<1−e−2m2/k0m2σ,(3.21)and the corresponding equation of state isUm2+k0m2σk0m2σ/m2 −1.(3.22)These models are supersonic for all space-like,and weak time-like currents,with the exception that in the null limit˜χ=0one has c L=c E=1.C.Equations of motionWe now derive the microscopic equations of motion for elastic cosmic string mod-els.It is convenient to start by deﬁning the quantityΘab≡˜Λγab−2∂˜Λthen recalling the deﬁnition of ˜χ,(3.11),onecanﬁnd the free string equations of motion in the usual (variational)way,obtaining(√−γΘab Γαµνx µ,a x ν,b =0.(3.24)Also in a similar way to what was done in section II,the eﬀect of the frictional forces is accounted for by introducing a term√βT 3b (3.26)(note that ˜Λis negative).Of course we now have a further equation for the scalar ﬁeld ˜ψ,namely ∂a √∂˜χγab ˜ψ;b =0.(3.27)Furthermore,the spacetime energy-momentum tensor and electromagnetic cur-rent will be given by√−γΘab x µ,a x ν,b δ(x −x (σ,τ))d 2σ(3.28)and√−γγab ∂˜Λ−(3)gT 00=a−˜Λ+2∂˜Λ−(3)gJ 0=−2ea∂˜Λ∂˜χ√∂˜χǫ˜ψ;0,(3.33)j≡−j1=−2e ∂˜Λǫ.(3.34)Again,for the reasons explained above,a particularly relevant situation will be that of a chiral current,that is one in whichγab j a j b=0.(3.35) This is equivalent to˜ψ′2=ǫ2˙˜ψ2,(3.36) and therefore it implies that∂ρ∂σ(3.37)and that the total(spacetime)charge and current are also equal.Note that in the chiral case one also has˜χ=0,2∂˜Λ−γ∂˜Λ−γ∂˜ΛD.The chiral limitWe now consider the(common)chiral limit of the two supersonic elastic models of Carter and Peter[10],deﬁned by the Lagrangian densities(3.17)and(3.20), respectively for the magnetic and electric regimes.Also,as we did in section II for the Witten model,we will interpret the charge coupling and the scalarﬁeld as being renormalised and neglect the coupling to external electromagneticﬁelds.Then,with our usual gauge choices and deﬁnitions of the damping and friction length-scales,the microscopic string equations of motion(3.24)simplify to[ǫ(1+Ψ)]˙+ǫaǫΨ,(3.44)andǫ(1+Ψ)¨x+ǫǫ ′+˙Ψ+2˙aµ0γ00.(3.46)That is,these are exactly the same equations of motion as those of Witten’s model(2.20–2.21)if one identiﬁes the corresponding scalarﬁelds,φ≡˜ψ.(3.47) Then,the worldsheet charge and current densities also coincide,ρw=qǫ˙˜ψ,(3.48)j w=q˜ψ′x(τ)=r(τ)(sinθ,cosθ,0);(4.1)we also need an ansatz for the scalarﬁeld˜ψ(orφ),which we will take to be˜ψ=√r2 =1,(4.4)¨r+ 1−n4t4c2.(4.6)Note that opposite signs of n correspond to left and right moving currents;naturally it always appears as n2in any relevant equation,and we will therefore be taking n to be positive.Inﬁgure1we plotted some relevant evolutionary properties of chiral supercon-ducting loops with diﬀerent n’s inﬂat spacetime.Note that these loops never collapse to zero size,and that their microscopic velocity is always less than unity (unlike in the Goto-Nambu case).Furthermore,there is a static solution withn=1t c˙r=0;(4.7)in this case the energy is equally divided between the string and the current.It should also be noted that energy is transferred back and forth between the string and the current as the loop oscillates.We can easily determine the following quantities(the averages are over one oscillation period)r22−n2,(4.8)t2c n2,(4.9)˙r2 =1E total =1−n,(4.11)12E2string2n;(4.12) note that the energy of these loops is E total/t c=2πµ.Finally,two other points that will have further relevance below.Firstly,a loops with a given conserved number n will reach a maximum microscopic velocity(and corresponding Lorentz factor)given by1˙r2max=1−4n2,γmax=µ0(F(τ)+nσ)t c.(5.1) The winding number per unitσand the function F are also constrained as before. In terms of these quantities the total energy of the loop can be written asE total=µ0ℓtotal=µ0a 1+n2t2c˙r a2r2 1a2r2 ¨r+(1−˙r2)4πnt cn=n is a variable parameter obeying0≤n=0corresponds to the Goto-Nambu case,while thev t2,ℓstring√n,namelyℓtotal1−n goes from zeroto unity we go from the Goto-Nambu case to the static case where the energy is split equally between the string and the current;the positive sign corresponds to the current branch,where the ratio of the energies in the string and in the current decreases until it vanishes whenn=2ℓstringℓstring−11/2.(5.9)In practice,it is not easily conceivable that in cosmological contexts loops can be formed with more energy in the current than in the string itself.Therefore, although for the sake of completeness we will be discussing the current branch in the remainder of this section,we will neglect it afterwards.Thus from(5.3)one obtains the evolution equation forℓ(ℓi,t i,n i,t) and other relevant quantities.As we will see below,a crucial quantity will be the the maximum velocity reached by each loop conﬁguration during it evolution, v max(ℓi,t i,n i).Inﬁgures3–5we plot the cosmological evolution of some relevant GUT-scale chiral circular loops.We should mention that in order to save space,only one out of every forty points resulting from the numerical integrations is plotted,and this is the reason why some plots show irregularities.Figure3shows some relevant properties of the evolution of chiral circular GUT-scale loops formed at t=t c;all have an initial total energy E total/2πµt c=10,but the distribution of the energy between the string and the current varies. Obviously,loops with higher currents will have smaller physical radii,and hence they will be less stretched by expansion and enter the horizon earlier,at which point they start oscillating—as can be conﬁrmed in3(a-b).Regarding the velocities,note the signiﬁcant diﬀerences between loops in the‘string branch’(which still reach fairly high microscopic velocities,but never v=1)and in the‘current branch’(which quickly become non-relativistic).Therefore the latter ones should deﬁnitely become vortons,and so it is perhaps fortunate that,as we pointed out above,we do not expect loops with such high currents to be produced in the early universe (at least,for GUT-scale networks).Note that in one of the cases shown the initial current is so high that the loop‘overshoots’and acquires a fairly large velocity,but friction quickly slows it down again.On the other hand,in the string branch the velocity is reduced with respect to the Goto-Nambu case,and a more detailed investigation will be needed to set14up some criterion deﬁning which velocities will allow vorton formation—recall that relativistic velocities will imply charge losses and it will therefore be unrealistic to make any deﬁnite claims or predictions about such cases.The evolution of the fraction of the loop’s energy in the current is particularly il-luminating(see3(c)).This will obviously decrease while the loop is being stretched, and it will start oscillating when the loop falls in side the horizon.The oscillations are around the state with equipartition of the energy between the string and the current,which as we saw corresponds to a static solution inﬂat spacetime.Note that the eﬀect of the friction force is to reduce the amplitude of these oscillations, so one can see that friction is in fact crucial for vorton formation.Naturally,loops with smaller velocities will undergo oscillations with smaller amplitudes,so again we conﬁrm that these are the strongest vorton candidates.Finally,we have plotted the parametern once the loop is‘free’—that is,much smaller than the damping length deﬁned in(2.22). On the other hand,radiative backreaction also tends to damp these energy os-cillations,and consequently increasen becomes a constant in this limit—hence its usefulness)˙r2 =1n2),(5.10)E string2E2total=1−3n;(5.12) the variance of the fraction of the energy in string is therefore∆E string4n).(5.13)Inﬁgure4we show chiral loops with the same initial conditions as3,but starting to evolve at the epoch t⋆when when friction becomes negligible[7].The diﬀerences are self-evident.Now,after aﬁrst period of growth of the total radius due to expansion,there is no mechanism forcing the loops to return this extra energy back to the medium when they fall inside the horizon.Consequently there is also no velocity damping(all loops will have microscopic velocities larger than0.5) and the energy oscillations between the string and the current always have a large amplitude—so thatthe region of the space of initial conditions that will originate them—because as we said the eﬀect of friction is to increasen∼1,in which case velocity is so small that friction does not signiﬁcantly aﬀect the loop.Note that asn and v needs to be looked at in more detail,and we shall do that in the next section.VI.CRITERIA FOR VORTON FORMATIONIn the previous section we saw that the evolution of chiral superconducting cosmic string loops depends sensitively on the conditions at formation.In particular,one would need to know in which cases one ends up with a vorton.Clearly,since we are not including radiative mechanisms at this stage,our crite-rion should be that loops whose velocity is always small(in a sense that will need to be made more precise)will become vortons,while those who are relativistic at some stage will suﬀer signiﬁcant charge losses,so that their fate cannot be clearly asserted until a rigourous quantum-mechanical treatment of these processes is available. Thus we will explore in more detail the phase space of possible initial condi-tions in order to determine relevant properties of these loops.Figure6shows the maximum microscopic velocity v max(ℓi,t i,n and to the base-ten logarithm of the initial string radius relative to the horizon;recall that we only consider loops having initially most of their energy in the string(in other words,loops in the string branch).Note that the friction length-scale corresponds to about−1.5in the vertical axis on theﬁrst plot,and to0on the last(where it is equal to the horizon, by deﬁnition).It can be seen that any loop initially larger than the horizon will inevitably become relativistic.This is essentially because expansion will(temporarily,at least) decrease the fraction of the loop’s energy in the current(and hencen(neglecting radiation),so we will need fairly high initial currents in order to get non-relativistic velocities.Finally,for the case of loops being produced with sizes between the friction length-scale and the horizon,which is of course the cosmologically relevant case during the16。

2.1狭义相对论基本原理.pdf

速应该各向不等，因而可看到干涉条纹。再使整个仪器转过 900，就应该发现条纹的
移到，由条纹移动的总数，就可算出地球运动的速度 v。迈克尔孙—莫来实验的装置
如图 2-1-2 所示，使一束由光源 S 射来的平行光，到达对光线倾斜 450 角的半镀银镜
面 M 上，被分成两束互相垂直的相干光。其中透射部分沿 MM 2 方向前进，被镜 M 2 反射回来，到 M 上，再部分地反射后沿 MT 进行；反射部分沿 MM1 方行进行，被镜反射
c 动，选 s ' 系固定在介质上，在 s ' 上观察，介质中的光速各方向都是 n ，所以光相对实
验室的速度 u 为
c +v c +v
u=
n
c v
=n 1+
v
1+ n
cn
c2
c + v 1 − v n cn
c +v− v
n
n2
=
c n
+
v1 −
1 n2
。
由此可知，由相对论的观点，根本不需要“以太”的假说，更谈不到曳引
c +v
c −v
传播速度为 n ，逆水为 n ；若水完全不带动以太，光对装置的速度顺逆水均为
c
c + kv
c − kv
n ；若部分被带动，令带动系数（曳引系数）为 k，则顺水为 n ，逆水为 n ，
k 多少由实验测定，这时两束光到达目镜 T 的时差为
t = 2l − 2l 4lkv
c − kv n
系数了。
迈克尔孙—莫来实验迈克尔孙—莫来于 1887 年利用灵敏的
S
M1 M2
M T
图 2-1-2

相对论原文（网摘）

相对论原文（网摘）论动体的电动力学大家知道，麦克斯韦电动力学 -- 像现在通常为人们所理解的那样 -- 应用到运动的物体上时，就要引起一些不对称，而这种不对称似乎不是现象所固有的。

比如设想一个磁体同一个导体之间的电动力的相互作用。

在这里，可观察到的现象只同导体和磁体的相对运动有关，可是按照通常的看法，这两个物体之中，究竟是这个在运动，还是那个在运动，却是截然不同的两回事。

如果是磁体在运动，导体静止着，那么在磁体附近就会出现一个具有一定能量的电场，它在导体各部分所在的地方产生一股电流。

但是如果磁体是静止的，而导体在运动，那么磁体附近就没有电场，可是在导体中却有一电动势，这种电动势本身虽然并不相当于能量，但是它 -- 假定这里所考虑的两种情况中的相对运动是相等的 -- 却会引起电流，这种电流的大小和路线都同前一情况中由电力所产生的一样。

诸如此类的例子，以及企图证实地球相对于“光媒质”运动的实验的失败，引起了这样一种猜想：绝对静止这概念，不仅在力学中，而且在电动力学中也不符合现象的特性，倒是应当认为，凡是对力学方程适用的一切坐标系，对于上述电动力学和光学的定律也一样适用，对于第一级微量来说，这时已经证明了的。

我们要把这个猜想（它的内容以后就称之为“相对性原理”①）提升为公设，并且还要引进另一条在表上看来同它不相容的公设：光在空虚空间里总是以一确定的速度V传播着，这速度同发射体的运动状态无关。

由这两条公设，根据静体的麦克斯韦理论，就足以得到一个简单而又不自相矛盾的动体电动力学。

“光以太”的引入将被证明是多余的，因为按照这里所要阐明的见解，既不需要引进一个具有特殊性质的“绝对静止的空间”，也不需要给发生电磁过程的空虚空间中的每个点规定一个速度矢量。

这里所要阐明的理论 -- 像其他各种电动力学一样 -- 是以刚提的运动学为根据的，因为任何这种理论所讲的，都是关于刚体（坐标系）、时钟和电磁过程之间的关系。

对这种情况考虑不足，就是动体电动力学目前所必须克服的那些困难的根源。

a-Galactosylceramide as a Therapeutic Agent for

a-Galactosylceramide as a Therapeutic Agent for Pulmonary Mycobacterium tuberculosis InfectionIsabel Sada-Ovalle1,Markus Sko¨ld1,Tian Tian1,Gurdyal S.Besra2,and Samuel M.Behar11Division of Rheumatology,Immunology,and Allergy,Brigham and Women’s Hospital and Harvard Medical School,Boston,Massachusetts; and2School of Biosciences,University of Birmingham,Edgbaston,Birmingham,United KingdomRationale:Invariant natural killer T(iNKT)cells are a unique subset of Tcells that recognize lipid antigens presented by CD1d molecules.Recentstudies have shown that iNKT cells can protect mice against Mycobac-terium tuberculosis(Mtb)infection.We sought to determine whetherpharmacological activation of iNKT cells by a-galactosylceramide(a-GalCer)could be used to treat tuberculosis(TB).Objectives:We hypothesized that a-GalCer,either alone or incombination with isoniazid,could be used to treat pulmonary TB.Methods:The ability of a-GalCer–activated iNKT cells to suppressMtb replication was evaluated using an in vitro coculture system.Totest its potency in vivo,mice infected with virulent Mtb were treatedwith a-GalCer alone or in combination with isoniazid.Measurements and Main Results:Quantitative colony-forming unitcounts were compared for both experimental systems.Our resultsshow that a-GalCer plus isoniazid controls bacterial growth betterthan a-GalCer or INH alone,and single or multiple a-GalCer admin-istrations prolong the survival of the mice infected via the aerosolroute.Conclusions:Our results demonstrate that a-GalCer administrationcan improve the outcome of Mtb infection,even when transmitted by the aerosol route.However,a combination of isoniazid and a-GalCer treatment has a synergistic effect on infection control. We conclude that more efﬁcient treatment of TB will be achieved through a combination of classic chemotherapy and modulation of the host immune response.Keywords:CD1d;antibiotics;natural killer T cells;tuberculosis;lipids Tuberculosis(TB)is caused by Mycobacterium tuberculosis(Mtb) and represents an important global threat to health,especially in developing countries where new and efﬁcient therapies are urgently needed.Although current antibiotic regimens against Mtb are effective against drug-susceptible strains,patients require long-term follow-up and can suffer severe side effects.In addition, the prevalence of multidrug-and extensively drug-resistant Mtb strains is on the rise(1).Treatment of drug-resistant bacterial strains is more complicated,requiring hospital supervision(2). Recent efforts to develop new therapeutic regimens are promis-ing,but their efﬁciency remains to be tested in larger populations. In the current study,we investigated whether the speciﬁc activa-tion of iNKT cells,which we have previously shown is capable of activating macrophages(M w)to suppress intracellular Mtb rep-lication,can act therapeutically against established pulmonary TB(3).Invariant natural killer T(iNKT)cells are a sublineage of T lymphocytes that are deﬁned by their expression of a canonical V a14-J a18T-cell receptor(TCR)a-chain.The ab-TCR expressed by iNKT cells recognizes self and foreign lipid antigens presented by the antigen-presenting molecule CD1d. iNKT cells inﬂuence host immunity during infectious diseases through production of soluble mediators,such as IL-4and IFN-g,by reciprocal NKT–dendritic cell(DC)activation and by elaboration of chemokines that recruit inﬂammatory cells(4–6).The discovery that CD1d presentation of a-galactosylcer-amide(a-GalCer)rapidly activates murine and human iNKT cells has greatly increased our understanding of the potential role that iNKT cells play in host immunity(7,8).The synthetic glycosphingolipid a-GalCer is a potent iNKT cell agonist,and even though it is not a natural ligand for iNKT cells,a-GalCer and its analogs are commonly used experimentally(9).iNKT cell activation by a-GalCer in vivo induces downstream activa-tion of several lymphoid and myeloid cell populations,including B and T cells,NK cells,M w,and DCs,which in turn can modify multiple immune responses(10–13).For example,a-GalCer has been used to analyze the immunomodulatory properties of activated iNKT cells in mice and patients with malignancies (14–16).Administration of a-GalCer activates both the innate and adaptive immune system and has raised the possibility of using a-GalCer for therapeutic purposes(8,17).The number of iNKT cells in the lung is increased after infection of mice with virulent Mtb(18).CD1d,which presents antigen to iNKT cells,is up-regulated by IFN-g and is also increased in the lungs of infected mice(19).We havepreviously(Received in original form December23,2009;accepted inﬁnal form May17,2010) Supported by the National Institutes of Health grant R01HL80312(S.M.B)and a Parker B.Francis Foundation postdoctoral fellowship(I.S.O).G.S.B.was supported by a Personal Research Chair from Mr.James Badrick,Royal Society Wolfson Research Merit Award,as a former Lister Institute-Jenner Research Fellow,the Medical Council,and The Wellcome Trust(084,923/B/08/7).M.S. was supported by the Swedish Heart Lung Foundation.Present address for I.S-O.is Immunochemistry Department,National Institute of Respiratory Diseases,Me´xico.Present address for M.S.is Department of Microbiology,Tumor and Cell Biology, Karolinska Institutet,Stockholm,Sweden.Present address for T.T.is Department of Dermatology,Brigham and Women’s Hospital and Harvard Medical School,Boston,Massachusetts. Correspondence and requests for reprints should be addressed to Samuel M. Behar,M.D.,Ph.D.,Division of Rheumatology,Immunology,and Allergy, Brigham and Women’s Hospital,Smith Building Room516C,One Jimmy Fund Way,Boston,MA02115.E-mail:sbehar@Am J Respir Crit Care Med Vol182.pp841–847,2010Originally Published in Press as DOI:10.1164/rccm.200912-1921OC on May27,2010 Internet address:shown that innate iNKT cells recognize Mtb-infected M w, produce IFN-g,and kill intracellular bacteria both in vitro and in vivo(3).Although these data suggest that iNKT cells can mediate protective immunity against TB,several laboratories have found that iNKT cells are not required for optimal immunity to Mtb(20,21).One explanation is that iNKT cells make only a small and possibly redundant contribution to antimycobacterial immunity.Another possibility is that after infection,iNKT cells become anergic,as has been shown after BCG and viral infection(22).Given the potential ability of activated iNKT cells to suppress bacterial growth,we wished to determine whether administration of a-GalCer could enhance the antibacterial activity of iNKT cells and whether a-GalCer could serve a role in the treatment of established disease. METHODSMiceSix-to8-week-old female C3H/HeJ(C3H)(highly susceptible to Mtb) and C57BL/6(B6)(relatively resistant to Mtb)mice were obtained from Jackson Laboratories(Bar Harbor,ME).All mice were housed in a BSL3facility under speciﬁc pathogen–free conditions in the Animal Biohazard Containment Suite(Dana Farber Cancer Institute,Boston, MA)and used in a protocol approved by the institution.Bacteria and In Vitro Infection of Peritoneal Macrophages Macrophages were harvested by peritoneal lavage4days after intraperitoneal injection of sterile3%thioglycolate medium.M w were puriﬁed by positive selection using CD11b-microbeads accord-ing to manufacturer’s directions(Miltenyi Biotec,Auburn,CA).The puriﬁed cells were95%F4/801CD11b1,as determined byﬂow cytom-etry.Puriﬁed M w(0.53106/well)were cultured in24-well plates in RPMI1640medium(Invitrogen Life Technologies,Carlsbad,CA) supplemented with10%fetal calf serum(HyClone,Rockford,IL), penicillin/streptomycin,L-glutamine,sodium-pyruvate,2-ME,nonessen-tial amino acids,essential amino acids,and N-2-hydroxyethylpiperazine-N9-ethane sulfonic acid(all from Gibco,Carlsbad,CA).Virulent Mtb (H37Rv)was grown to mid-log phase in Middlebrook7H9medium supplemented with10%albumin/dextrose/catalase(BD Biosciences, San Jose,CA).Bacteria were opsonized for5minutes using RPMI 1640with2%human serum(Gemini Bio-Products,West Sacramento, CA),10%fetal bovine serum,and0.05%Tween80and then washed twice with complete medium without antibiotics.Bacteria were passed through a5-m m syringeﬁlter(Millipore,Billerica,MA),counted in a Petroff-Hausser chamber,and added to enriched M w for2hours before extensive washing to remove extracellular bacteria.The length of infection was2hours for all experiments.Recombinant mouse IFN-g(US Biological,Swampscott,MA),a-GalCer,and a-C-GalCer were used at the concentrations indicated.Colony-Forming Unit Determination(In Vitro Model) Bacterial growth was quantiﬁed72hours after coculture with naive splenocytes with or without IFN-g and/or a-GalCer(Day4).The cells were lysed after removing the supernatant by adding distilled water. Serial dilutions were plated on Middlebrook7H11agar plates.The number of bacteria contained in the supernatant was less than10%of the cell-associated colony-forming units(CFU),independently of whether splenocytes were added.The colonies were enumerated after 3weeks at378C.Bacteria and InfectionsVirulent M.tuberculosis(Erdman strain)were passed through mice and subsequently grown once in Middlebrook7H9supplemented with the oleic acid–albumin–dextrose complex and stored at808C.For each experiment an aliquot was thawed,sonicated twice for10seconds with a cup horn sonicator,and then diluted in0.9%NaCl20.02%Tween80. Mice were infected via the aerosol route as described previously(23). For intravenous infections,mice were injected via the lateral tail vein with0.253106to4.03106live mycobacteria.The inoculum was conﬁrmed by plating.Treatment of Mice with a-GalCera-GalCer was prepared in a vehicle of0.5%polysorbate20.The mice were injected with a low(100m gÁkg21)or high(500m gÁkg21)dose of a-GalCer,or injected with control vehicle.The following treatment regi-mens were tested:(1)intraperitoneal injection of100m gÁkg21a-GalCer on Days5,3,and1before aerosol infection;(2)intraperitoneal injection of100m gÁkg21a-GalCer on Days1,5,and9after aerosol infection;(3) intratracheal injection of100m gÁkg21a-GalCer on Day1after aerosol infection;(4)intraperitoneal injection of500m gÁkg21a-GalCer on Day1 after aerosol infection;(5)intraperitoneal injection of500m gÁkg21 a-GalCer on Day1after aerosol infection and then again every30th day;(6)intraperitoneal injection of500m gÁkg21a-GalCer on Day30 post aerosol infection and then again every30th day.a-GalCer and Antibiotic TreatmentGroups of C3H/HeJ mice were infected via the intravenous route and injected with a low dose of a-GalCer or vehicle on Day1post infection (p.i.).On Day14p.i.,isoniazid(100mg/L)was added to the drinking water.The drinking water was changed twice weekly during the treatment period and the mice had access to the water ad libitum. The isoniazid treatment was stopped on Day28p.i.and the CFU was determined in lung and spleen on Day36p.i.Measurement of IFN-g Lung ProductionBefore removal,lungs were perfused by injecting5to10ml of sterile PBS into the right ventricle of the heart after severing the inferior vena cava.The lungs were homogenized in0.9%NaCl20.02%Tween80 with a Minibeadbeater-8and centrifugation for20minutes at3,000 rpm,then supernatants were recovered and IFN-g was analyzed by a standard ELISA sandwich.CFU Determination(In Vivo Model)Three,5,or12weeks after infection,mice were killed and their left lung and spleen were aseptically removed and individually homoge-nized in0.9%NaCl–0.02%Tween80.Viable bacteria were enumer-ated by plating organ homogenates onto7H11agar plates.Colonies were counted after3weeks.StatisticsData were expressed as parisons of data among experimental groups were performed using analysis of variance with Bonferroni post test.A survival analysis was performed using Kaplan-Meier method and comparisons were done with log-rank test.Values of P,0.05were considered to be statistically signiﬁcant. RESULTSa-GalCer–Activated Splenocytes Reduce Intracellular Replication of Mtb In VitroWe have previously shown that nonimmune splenocytes have innate antimycobacterial activity that is mediated by iNKT cells,which recognize Mtb infected M w and restrict intracellular bacterial growth(3).Although CD1d expression by the infected M w is required,which implies cognate recognition(3),it is uncertain whether CD1presents a microbial antigen,or alter-natively,whether cytokine production costimulates weak rec-ognition of an endogenous(self)antigen(24).Because only1to 2%of splenocytes are iNKT cells,we wondered whether pharmacological activation of iNKT cells with a-GalCer would enhance the growth suppression of Mtb mediated by iNKT cells in vitro.Coculture of naive splenocytes with Mtb-infected M w reduced the number of viable CFU as reported previously (Figure1A)(3).Addition of a-GalCer led to a further re-duction in CFU,as did the addition of IFN-g,and adding both a-GalCer and IFN-g led to an additive,and possibly coopera-842AMERICAN JOURNAL OF RESPIRATORY AND CRITICAL CARE MEDICINE VOL1822010tive,effect on CFU control.Treatment with a-GalCer was associated with a dose-dependent increase in IFN-g production (Figure1B).Thus,although iNKT cells have the physiological potential to recognize infected M w,their pharmacological activation by the synthetic lipid a-GalCer leads to a more potent mycobactericidal effect.Systemic Therapy with a-GalCer Prolongs the Survivalof Susceptible Mice after Low-Dose Aerosol Infectionwith M.tuberculosisWe next wished to determine the potential of a-GalCer to treat mice with pulmonary TB.To observe protection,we selected C3H mice,which are a susceptible mouse strain that develops extensive lung pathology and succumbs to infection earlier than B6mice(25–27).Previously,we demonstrated that a single dose of a-GalCer(100m gÁkg21)administered intraperitoneally within5days of Mtb infection by the intravenous route was effective in prolonging the survival of susceptible C3H mice (28).However,a-GalCer administered by the intraperitoneal route did not protect mice against low-dose aerosol(LDA) infection with virulent Mtb(Figure2A).There are several important differences between the systemic and pulmonary routes of infection that may affect the efﬁcacy of a-GalCer. We hypothesized that a-GalCer–activated iNKT cells acted locally.Therefore,a-GalCer(100m gÁkg21)was administered intratracheally after LDA infection with Mtb.a-GalCer-treated mice had prolonged survival in two separate experiments (Figure2A).These data indicate that locally activated iNKT cells can provide protection against LDA Mtb infection.Ishii and colleagues reported that intraperitoneally adminis-tered a-GalCer(10m g/100m l vehicle)has a protective effect on the lung after bleomycin treatment(29).Based on these results, we analyzed whether a high dose of a-GalCer(500m gÁkg21) administered systemically protected mice challenged with LDA pared with mice treated with vehicle alone,a-GalCer administered intraperitoneally on Day1post infection pro-longed the survival of susceptible C3H/HeJ mice(Figure2B). The mean survival time(MST)of vehicle-treated mice was60 days.In contrast,the mice that received a single injection of a-GalCer(500m gÁkg21)had a MST of106days.These data show that systemic administration of high-dose a-GalCer pro-tects mice against pulmonary TB.Having established that systemic a-GalCer could protect mice against LDA Mtb infection,we next determined whether repeated administration of a-GalCer would provide longer-term protection.Mice were given a-GalCer on Day1after Mtb infection and then administered a-GalCer every30days, a treatment regimen that signiﬁcantly prolonged their survival compared with vehicle-treated control mice(MST5124d vs. 31d;P50.0009).However,repeated monthly injections with a-GalCer had only an incremental effect on the survival compared with animals injected with a single dose of a-GalCer on Day1after LDA infection(MST5124d vs.106d;P5not signiﬁcant)(Figure2C).Thus,similar to the low-dose a-GalCer treatment regimen after intravenous MtbinfectionFigure2.Treatment with a-galactosylceramide(a-GalCer)(100m gÁkg21or500m gÁkg21)signiﬁcantly prolongs the survival of mice infected bythe aerosol route.(A)Survival of mice after the administration ofa-GalCer(100m gÁkg21)by the intraperitoneal or intratracheal route(n510).Mice were divided in four groups.One group(solid diamonds)received a-GalCer group by intraperitoneal administration on Days25,23,and21.A second group(solid squares)received a-GalCer groupby intraperitoneal administration on Days1,5,and9.A third group(closed circles)received a-GalCer group by the intratracheal route onDay1.Mice were infected with Mycobacterium tuberculosis(Mtb)bylow-dose aerosol(LDA)on Day0.(B)Vehicle(open circles)or a-GalCergroup(500m gÁkg21)(solid circles)was administered intraperitoneally1day after LDA infection with Mtb.(C)Survival of mice after theadministration of a-GalCer(500m gÁkg21)by the intraperitoneal route(n510).No animals died in the uninfected group treated witha-GalCer.Mice received vehicle(open circles),a-GalCer on Day1byintraperitoneal administration(solid circle),or multiple doses ofa-GalCer(solid squares)starting on Day1and then every30days.(D)Mice(solid diamonds)received multiple intraperitoneal administra-tions starting on Day30and then every30days.C and D are from thesame experiment and the data are separated for clarity.Survivalanalysis was performed using Kaplan-Meier method and comparisonswere done with log-rank test.*P,0.05,***P,0.0005.Sada-Ovalle,Sko¨ld,Tian,et al.:iNKT Cells,INH,and Tuberculosis843(28),a single dose of a-GalCer injected on Day1after LDA Mtb infection signiﬁcantly prolonged the survival of the infected mice and repeated administration did not provide any additional beneﬁt.Importantly,treatment with a-GalCer did not diminish the survival of uninfected mice and there were no deaths in mice repeatedly treated with a-GalCer,even after200days of observation(data not shown).This is consistent with Kimura and colleagues,who found that although a-GalCer treatment attenuated the development of bleomycin-induced pulmonary ﬁbrosis,it did not appear to have any adverse effects on the pulmonary architecture(29).Three weeks after a-GalCer treatment of infected mice,no histopathological changes in the lung were observed compared with vehicle-treated control mice(data not shown).However,this does not rule out other subtle changes in the number or volume of granuloma or changes at later time points(28).These results demonstrate that systemic activation of iNKT cells can provide protection to susceptible mouse strains against LDA Mtb infection.a-GalCer Treatment of Susceptible Mice with EstablishedMtb Infection Prolongs Their SurvivalThe ability of a-GalCer to protect mice against LDA Mtb infection suggests that it could be useful as an adjunct treatment against TB.A critical issue is whether a-GalCer had efﬁcacy against established TB disease.To evaluate this question,treatment of mice infected with a low dose of aero-solized Mtb was postponed until Day30post infection.At this time point,the bacterial counts in the lung are approximately 10,000-fold greater than the initial inoculum,and the immune response has controlled bacterial replication leading to the establishment of the plateau phase of the infection.Starting on Day30,mice were treated with a-GalCer(500m gÁkg21) every30days.Delayed administration resulted in a signiﬁcant increase in survival compared with vehicle control mice(MST5 56d vs.31d;P50.02)(Figure2D).This indicates that act-ivated iNKT cells can alter the course of established TB infection.a-GalCer Administration Increases Lung IFN-g Production and Controls Bacterial ReplicationInjection of a-GalCer into naive mice leads to rapid but transient activation of iNKT cells(22).Still,we observed a long-term beneﬁcial effect after a single injection of a-GalCer in Mtb aerosol-infected mice.A dose-dependent stimulation of IFN-g (Figure1B)but not IL-4(data not shown)was observed when a-GalCer is added to a coculture of splenocytes and Mtb-infected M w.We hypothesized that the beneﬁcial effect of iNKT cells is mediated in part by IFN-g production.To determine whether iNKT cell activation induces long-term IFN-g production in the lung,a-GalCer(500m gÁkg21)or vehicle was injected intraperi-toneally into resistant B6or susceptible C3H mice24hours after LDA Mtb infection.Lung CFU and IFN-g production were measured in total lung homogenates3weeks post infection. Although the data did not reach statistical signiﬁcance,the IFN-g concentration was elevated in lung homogenates3weeks after a-GalCer treatment compared with vehicle-treated control mice (Figure3A).Importantly,the bacterial burden in the lungs of mice treated with a-GalCer was signiﬁcantly reduced3weeks after aerosol infection compared with vehicle-treated control mice(B6and C3H;Figures3B and3C).In addition,treatment of B6mice with a-C-GalCer(30),an analog of a-GalCer that has greater Th1-inducing capability,led to a greater CFU reduction (Figure3B).a-GalCer Has an Additive Effect When Administeredwith IsoniazidWe have shown that a-GalCer treatment ameliorates pulmo-nary TB and prolongs survival of susceptible mice,even in those with established pulmonary TB.However,a-GalCer treatment did not eradicate the bacterium or fully cure infected mice, indicating that the use of a-GalCer as a single therapeutic agent is not feasible.Because immune modulation using a-GalCer and conventional antibiotics reduces bacterial growth by dis-tinct mechanisms,we considered whether a-GalCer could have a role as an adjunct therapy.Therefore,we determined the efﬁcacy of a-GalCer when administrated with or without the ﬁrst-line antibiotic isoniazid(INH).We were particularly in-terested in testing this combination in a different disease model, one in which there was signiﬁcant systemic disease.Therefore, we infected mice by the intravenous route to rapidly dissemi-nate the bacteria and establish a systemic infection with a high peripheral bacterial burden.Five weeks after Mtb infection,the combination of a-GalCer and INH signiﬁcantly reduced bacte-rial burden in spleen and lung tissue.Importantly,even under conditions of disseminated disease with a high bacterial burden, the combination of a-GalCer plus INH had an additive effect in controlling bacterial growth in the lungs and in the spleen (Figure4).Our results suggest that a combination of traditional chemotherapy and modulation of the immune response during pulmonary TB can be used for more efﬁcient control of Mtb replication.DISCUSSIONThe promise of immunotherapy,an approach that may have important implications for drug-resistant disease(31,32),has yet to show itself as an important part of the arsenal against TB. Although IFN-g,IL-2,IL-12,and thalidomide have been tried as immune modulators in patients with pulmonary TB,the results of experimental studies and clinical trials have been only moderately encouraging(33–37).Although many clinical stud-ies using IFN-g,IL-12,and thalidomide have demonstrated the potential of these agents to enhance immune responses to infection(38,39),a clinical response has beenﬂeeting.Obtain-ing a therapeutic effect will require unraveling the mechanism of action in addition to optimizing the timing,dose,and route of administration.The complex and myriad effects ofcytokinesmost likely explain the difﬁculty in implementing the clinical use of these different agents.Immune therapy with a-GalCer has also been suggested as a therapeutic option for human diseases,including multiple sclerosis,type1diabetes,rheumatoid arthritis,and lung cancer (16,40,41).Given the low frequency of these iNKT cells,it is remarkable that their activation could change the outcome of disease.Furthermore,given the complex interactions between Mtb and host immunity within the microenvironment of infected foci,simple activation of iNKT cells with a-GalCer in vivo is unlikely to be sufﬁcient to elicit a curative response.A more realistic strategy would be to combine a-GalCer with conventional antibiotics.Pharmacological activation of iNKT cells by a-GalCer modulates adaptive immunity to several different microorgan-isms,including Mtb,Pseudomonas aeruginosa,Cryptococcus neoformans,and several different viruses(3,42,43).However, it has also been shown that speciﬁc iNKT cell activation with a-GalCer can exacerbate disease caused by Leishmania dono-vani infection(44).Therefore,the use of synthetic glycolipids to potentiate the function of iNKT cells must be carefully studied. Weﬁnd that a-GalCer and INH have an additive effect in reducing the bacterial burden in Mtb-infected mice,and that a-GalCer prolongs the survival of infected mice with estab-lished pulmonary TB after Mtb infection via the respiratory route.How does a-GalCer modify the natural course of pulmonary TB?We have previously shown that the ability of a-GalCer to prolong the survival of Mtb-infected mice and to ameliorate disease requires CD1d(28)and is therefore dependent on the action of iNKT cells.We have recently shown,using an in vitro model of infection,that iNKT cells can kill intracellular Mtb and induce host protection after being adoptively transferred into mice infected with Mtb via the aerosol route(3).However, other actions of a-GalCer may be important.For example,Fujii and colleagues have shown that intravenous administration of a-GalCer into mice induces DC maturation.This effect is mainly mediated by TNF-a and IFN-g,and mature DCs can induce greater T-cell responses because of more efﬁcient antigen presentation than exposure to mycobacterial antigens alone(45).Recently,a-GalCer incorporation into BCG has been shown to enhance the conventional CD81T-cell response;thus,it does appear that iNKT cell activation is modulating T-cell priming(46).The ability of iNKT cells to produce IFN-g after a-GalCer stimulation is one of their most important features to mediate host protection and may have therapeutic implications(47,48). Given the importance of IFN-g in controlling Mtb growth and the fact that a-GalCer administration induces IFN-g production by iNKT cells and by NK cells after downstream activation(49), one explanation for how a-GalCer ameliorates pulmonary TB may simply be via the induction of IFN-g.However,our in vitro data show that a combination a-GalCer and IFN-g is more efﬁcient in controlling bacterial growth than a-GalCer or IFN-g treatment alone(Figure1A).This suggests that a-GalCer–activated iNKT cells reduce Mtb replication via an IFN-g independent mechanism,perhaps via direct effector functions.In this study we wanted to determine whether a-GalCer could ameliorate TB after infection via the respiratory route and if a-GalCer could ameliorate established pulmonary TB. Therefore,we infected mice via the aerosol route to mimic the natural route of Mtb infection and we used a high dose of a-GalCer(500m gÁkg21),which has been shown by others to inﬂuence the immune response in lung tissue(29).We found that a single dose of a-GalCer systemically or intratracheally signiﬁcantly prolonged the survival of LDA Mtb-infected mice. We also observed that delayed administration of a-GalCer dramatically improved the outcome of established infection as determined by survival.We have previously shown that repeated a-GalCer admin-istration does not have a greater beneﬁcial effect on survival after intravenous Mtb infection than a single a-GalCer in-jection.In the present study weﬁnd similar results using a model of LDA Mtb infection.The LDA Mtb-infected group that received multiple a-GalCer administrations30days apart lived only18.5more days compared with the infected group that received a single a-GalCer dose.Chiba and colleagues have previously shown using an in vivo model of Mycobacterium bovis bacille Calmette-Gue´rin(BCG)infection that the re-sponsiveness of NKT cells changes during the natural course of the infection,including a transient period of anergy(22).If a-GalCer activation of NKT cells also leads to a period of anergy,the timing of repeated a-GalCer administration could be a critical variable that affects the NKT cell response.At present,one of the most important approaches against TB infection is the design of new therapeutic options,including adjuvants and vaccines.Although current treatment is effective against susceptible Mtb strains,the emergence of multidrug-and extensively drug-resistant strains requires the use of new strategies that can enhance the immune response.We show that the use of a-GalCer as adjuvant therapy inﬂuences the immune response by enhancing iNKT cell production of IFN-g,which presumably activates lung M w to kill Mtb and induces DC maturation to improve antigen presentation to T cells.Similar effects have been observed in other infection models(50–52). Using a clever strategy to exploit the adjuvant properties of a-GalCer clinically,Venkataswamy and colleagues incorpo-rated a-GalCer into the cell wall of BCG.A better immune response was elicited by the modiﬁed BCG(46).New and efﬁcient antibiotics are likely to emerge on the market to help ﬁght pulmonary TB.Unfortunately,there will be an ongoing battle between any new anti-TB drug candidate and the de-velopment of drug resistance.The inclusion of immunomodu-latory agents as adjuvant therapy may prove to be beneﬁcial in the treatment of TB.Because a-GalCer treatment in people with cancer has been proven to be safe(53),we believe that further studies with a-GalCer are warranted todetermine。

05第五章相对论

第5章相对论基础5-1 相对性原理1. 伽利略相对性原理● 伽利略相对性原理：一切彼此作匀速直线运动的惯性系，对于描写机械运动的力学规律来说是完全等价的，并不存在任何一个比其它惯性系更为优越的惯性系，与之相应，一个惯性系的内部所作的任何力学的实验都不能够确定这一惯性系本身是在静止状态，还是在作匀速直线运动。

● 伽利略相对性原理解释：在一个惯性参照系K 中，质点的质量、位矢、速度、加速度和质点所受的力分别为：Fa v r m ,,,,，在另一个相对于参照系K 以速度R v 作匀速直线运动的惯性参照系K '中，该质点的质量、位矢、速度、加速度和质点所受的力分别为：F a v r m ''''' ,,,,。

伽利略相对性原理指出，无论在参照系K 中，还在在参照系K '中，描写机械运动的力学规律的牛顿定律应该具有相同的形式：在参照系K 中：a m F =在参照系K '中：a m F ''='● 伽利略相对性原理来源：在经典力学的时空观是绝对时空观，绝对时空观得到的坐标变换为伽利略坐标变换，由伽利略坐标变换得到，在参照系K 和参照系K '中的加速度相等，经典力学认为，在参照系K 和K '中，质点的质量和所受的力都相等，所以在参照系K 和K '中描写机械运动的力学规律的牛顿定律具有相同的形式，所以经典力学的概念满足伽利略相对性原理。

伽利略坐标变换：t v r r R -='，t t ='得加速度变换为：a a=' 经典力学认为：m m ='，F F ='所以由参照系K 中的牛顿定律：a m F =可以推出参照系K '中的牛顿定律：am F ''=' 两个参照系中的牛顿定律形式相同2. 洛伦兹坐标变换● 洛伦兹坐标变换的来由：根据伽利略坐标变换，电磁学方程在参照系K 和K '中具有不同的形式，电磁学方程不满足相对性原理，为了使电磁学方程满足相对性原理，洛伦兹提出了洛伦兹坐标变换。

百度_相对论吧_[原创-假说]西洋物理学错误观点大全(更新为15个)

2、正确观点：在同一星球上，无法区分静止和匀速运动；在不同的星球上，甚至无法区分匀速运动和加速运动。
3、证据：在地球和火星上分别停放俩火车，俩火车上牛顿运动定律都绝对精确成立，但俩火车之间却在做相对加速运动。
4、独创、首创。广义相对论表明无法区分加速运动和引力场，但错误地将它在同一星球上“使用”。他没有将伽利略相对性原理限制在“同一星球上”，没有将广义相对性原理限制在“星球之间”。
西洋物理学错误观点大全
一、牛顿力学中的加速度的参照物
1、西洋观点：牛顿认为其“水桶实验”证明了绝对空间的存在，认为水相对“绝对空间”加速运动时，水面不再水平。即牛顿定律中的加速度是相对“绝对空间”的。
2、正确观点：牛顿“水桶实验”并不能证明绝对空间的存在，水相对地球加速运动时，水面不再水平。
3、证据：电子围绕原子核加速运动（向心加速度），并不辐射电磁波；外力对电荷作的功正好等于电荷的动能，没有能量损失；在电磁波中，辐射的瞬时功率最大时，发射塔中电荷的加速度却是零，瞬时功率为零时，电荷的加速度却最大。
4、独创、首创
十二、电容器间的电场强度和两端的电压
3、证据：电流既有“位移电流”又有“传导电流”，与电流不同，“磁流”只有“位移磁流”没有“传导磁流”。因此人们只注意到了磁场的“磁容性”（弹性），即认为磁场强度（位移）永远和电流强度（力）成正比！而事实上“变化的磁场”就是“位移磁流”，磁场同样有“磁感性”（惯性），因此电流强度同样可以让磁场产生“加速度”（而不再是形变）。比如在电磁波中，振源的电流强度最大时，振源处的磁场强度却是零，符合“面积定律”。
4、原创但非独创，北京大学孟庆信也表示，在计算光速的过程中，让公式E=BV和B=EV/CC中的E和B同速前进是件很奇怪的事。肖军也表示，不能将公式E=BV计算出来的E再代回公式B=EV/CC中（求公式E=BV中的B）。我在与肖军的辩论时说：将公式E=BV计算出来的E再代回公式B=EV/CC中（求公式E=BV中的B），那就是找死。（当然，我和肖军辩论的具体情况与此不同，我们议题中的B=EV/CC中的E是库仑电场，B是运动电荷产生的（感生）磁场；我们议题中的E’=BV中的E’是上述（感生）磁场（再）运动时产生的（感生）电场，此E’和彼E不可比。）

MARKSCHEME M11 P1 TZ2

8
Alternative methods Candidates will sometimes use methods other than those in the markscheme. Unless the question specifies a method, other correct methods should be marked in line with the markscheme. If in doubt, contact your team leader for advice.
–3–
M11/5/MATHL/HP1/ENG/TZ2/XX/M
Instructions to Examiners
Abbreviations M (M) A (A) R N AG Marks awarded for attempting to use a correct Method; working must be seen. Marks awarded for Method; may be implied by correct subsequent working. Marks awarded for an Answer or for Accuracy; often dependent on preceding M marks. Marks awarded for an Answer or for Accuracy; may be implied by correct subsequent working. Marks awarded for clear Reasoning. Marks awarded for correct answers if no working shown. Answer given in the question and so no marks are awarded.

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

20110113 Alpha 版亲爱的朋友，非常欢迎你来到相对论吧。

这是一个具有深厚文化底蕴、科学理论基础知识扎实的贴吧。

在这里，许多吧友们都是值得尊敬的老朋友、他们有战斗在物理学第一线的科研、教学工作者和热爱物理的在校学生，也有众多的业余科学爱好者。

如果你有什么理论上的疑问，尽管他们未必每日在线，总有吧友为你热心地解答。

在此，我们对各位吧友所作的辛勤耕耘表示由衷地感谢和尊重！你的到来给我们的贴吧带来新的活力，更希望对物理有爱好的同志申请加入贴吧，成为相对论吧这个大家庭中的一员。

让我们来一起感悟相对论和物理科学的独特魅力，相互交流，相互学习，逐步提高水平，一起分享我们的思想成果，体会当代的物理学赋予相对论新的使命。

我们将第一时间转载来自科学前沿阵地传来的激动人心的消息。

相信你是对物理怀着强烈的好奇心而走进了物理学这片内涵深厚、潜力无限的领地，来到了相对论吧。

希望我们相对论吧能够引领或者帮助大家更好的畅游于物理学的世界。

无论你来自哪里，年龄多大，物理学习到什么程度，我们都是为了一个共同的理想和目标走到一起来的。

衷心地希望各位吧友分享自己在学习、教学以及科研过程中的心得，积极参与贴吧的各种讨论。

有些新来的吧友可能觉得自己水平有限，对环境不熟悉，发贴时很拘束。

在这里我想对这些朋友说：没有人生下来就是物理学大师（爱因斯坦也不例外，虽然他的理论发现很卓越），没有人生下来就是天才，如果要想成为一个令人尊敬的大师，成为闪光的天才，那么，这里也许将会给你提供一个很好的平台。

我们应该知道，每个当今的科研工作者，甚至知名科学家，在曾经的学习过程中都是由浅入深，从牛顿三定律，弹簧木块和斜面开始，逐渐走向更加深邃，或者更加复杂的当代理论的。

所以，希望这些朋友发贴时请不要有顾忌，问题也好，困惑也好，牢骚也好，请大胆的说出来。

相信吧里的各位“前辈”或“高手”也一定会以最友善的态度毫无保留的与你一起分享他们自己的经验。

当然，如果你是一位有志于从事物理的而又刚入行的学生，或者打算严肃系统学习自然科学的爱好者，那么我们总是鼓励以多看书、多思考、多演算、以及和周围的同学老师讨论为主，而以上网为辅。

虽然我们是相对论吧，但吧内讨论的内容实际上包含物理学相当多领域，尤其是物理学的另一个支柱理论：量子理论。

所以我们欢迎大家对物理学、自然科学、工程科学等各个方面的问题进行讨论，发表看法。

事实上，这里已经聚集了不少各个领域的专家。

祝愿大家在这良好的气氛和讨论环境中有所收获，有所启迪。

为了帮助大家更好地在相对论吧交流，我们特意制作了这份手册。

手册内容包括：1贴吧篇 ...................................................................................................................................................... 2 常驻吧友介绍...................................................................................................................................... 2丽雅 Leah ........................................................................................................................................ 2CloudK ............................................................................................................................................. 2南澳洲 ............................................................................................................................................. 3Inempty ............................................................................................................................................ 3 LostAbaddon .................................................................................................................................... 3 teamark ............................................................................................................................................ 3 Fishwoodok...................................................................................................................................... 3鲁来豪夫 ......................................................................................................................................... 3 台湾 PiPi ......................................................................................................................................... 3 李微商 ............................................................................................................................................. 3Schrodinger ..................................................................................................................................... 3 申请会员须知...................................................................................................................................... 4 资源篇 ...................................................................................................................................................... 4 视频资源总集...................................................................................................................................... 4物理视频 ......................................................................................................................................... 4 数学视频 ......................................................................................................................................... 7 科普纪录片 ..................................................................................................................................... 7图书资源总集...................................................................................................................................... 9物理书籍 ......................................................................................................................................... 9 数学书籍 ....................................................................................................................................... 11贴吧篇常驻吧友介绍在此列举部分本吧高手的名单，他们发的帖子有很高的参考价值，可信度高。

吧友们浏览他们的帖子时可以放心学习。

丽雅 LEAHライス University 博士、讲师，主攻宇宙学，兼修粒子物理。