Black Hole Information

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BLACK HOLE INFORMATION ?Don N.Page CIAR Cosmology Program Theoretical Physics Institute Department of Physics University of Alberta Edmonton,Alberta Canada T6G 2J1Internet:don@page.phys.ualberta.ca (1993May 10,revised July 31)Abstract Hawking’s 1974calculation of thermal emission from a classical black hole led to his 1976proposal that information may be lost from our universe as a pure quantum state collapses gravitationally into a black hole,which then evaporates completely into a mixed state of thermal radiation.Another pos-sibility is that the information is not lost,but is stored in a remnant of the evaporating black hole.A third idea is that the information comes out in nonthermal correlations within the Hawking radiation,which would be ex-pected to occur at too slow a rate,or be too spread out,to be revealed by

any nonperturbative calculation.

1.Hawking’s Proposed Loss of Information

Hawking’s1974calculation[1,2]of the emission from a stationary classical black hole was soon shown to give uncorrelated thermal emission in each mode[3-5].If a semiclassical approximation were used so that the black hole shrinks in a quasista-tionary way during the evaporation,one would still expect nearly thermal emission with high entropy,though even this calculation(without quantizing the geometry) has not been done precisely in four dimensions.As a result of these calculations and expectations,Hawking argued[5]that the semiclassical approximation should be good until the black hole shrunk near the Planck mass,and then there would not be enough energy left for the information that collapsed into the black hole to come back out.Thus a pure quantum state that underwent gravitational collapse into a black hole that subsequently evaporated away would end up as a mixed quantum state of Hawking radiation.Hawking proposed that the process would be described by a superscattering operator$that would take initial density matrices into?nal density matrices in a nonunitary way,generically increasing the?ne-grained entropy S≡?T r(ρlnρ):

ρfinal ab =$cd abρinitial

cd

,(1)

with a sum over the repeated indices c and d,where$cd ab would not have the usual

unitary form S c aˉS d b in terms of a unitary S matrix.

This process would correspond to the loss of information in the sense that from an

initial pure state,one could not predict any single?nal pure state with certainty.A

pure state may be represented by a normalized vector|ψ in the Hilbert space of the

quantum system(here,the universe,or at least our connected component of it).A

pure state can also be represented by a statistical state or density matrix(in general,

a positive-semide?nite Hermitian unit-trace operator or matrix acting on the vectors

in the Hilbert space)which when pure has the formρ=|ψ ψ|.Hence in this pure

caseρis a rank-one projection operator withρ2=ρand therefore with T rρ2=1

and entropy S=0as well as the general normalization(unit-trace)requirement

T rρ=1.A pure state may be contrasted with a mixed state,which cannot be

represented by a single vector in the Hilbert space,but which can be represented

by a statistical state or density matrixρ= n p n|ψn ψn|=ρ2with more than one nonzero eigenvalue p n,each of which can be interpreted to be the probability

of measuring the mixed state to be in one of the corresponding orthonormal pure

states|ψn .(It can be misleading,e.g.,in the EPR‘paradox,’to say that a system

in a mixed state is actually in one of its component pure states|ψn with probability

p n,because the system might instead actually be correlated with another system in

a composite system,and the composite system as a whole could even be in a pure state.)By the positive-semide?nite and unit-trace properties of general density matrices,the p n’s are nonnegative and add up to unity,and one can readily see that a mixed state has T rρ2<1and S≡?T r(ρlnρ)>0.

If one makes a complete measurement of a system,by which I mean the mea-surement of a nondegenerate observable(represented by some Hermitian operator with totally nondegenerate eigenvalues),a pure state is the only kind that can give a de?nite result with certainty(unit probability).A pure state,and only a pure state, has the property that one can predict with certainty the result of some complete measurement of the system.For one indeed to be able to predict with certainty,one needs the measured observable to have one of its eigenvectors proportional to the Hilbert space vector|ψ representing the pure state,so of course not every observ-able will give a uniquely predictable result.(This is a manifestation of the quantum uncertainty that applies even to pure states.)However,for any pure state,there do exist nondegenerate observables(in the sense of Hermitian operators but not,in general,in the sense of what is experimentally and practically possible)which would give de?nite results.

For example,suppose one had access to a su?ciently large ensemble of identical systems in the same(initially unknown)pure state and could in principle measure enough observables.The?rst observable one randomly chose to measure would generally not give de?nite results(i.e.,one would get di?erent individual results when one measured di?erent members of the ensemble with it).Nevertheless,one could eventually?nd some observable which would always give the same de?nite result when applied to members of the ensemble.(This would not be a unique observable,since only its eigenvector proportional to the pure-state vector would be uniquely determined,up to a complex multiplicative constant.Furthermore,this member of the preferred class of observables would only be determined to some?nite accuracy if only a?nite sequence of measurements were made to?nd a?nitely good empirical approximation to one of these preferred observables.)

It is in this sense that one can say that complete information(the maximum allowed by quantum mechanics)exists for a system in a pure state.

On the other hand,for a mixed or impure state there is no nondegerate observable that would have a unique value with unit probability.In other words,one cannot predict with certainty the result of any complete measurement of a system in a mixed state.In this sense one says that mixed states have less than maximal information. Of course,in another sense one could say that the actual density matrix gives all of the information possible about the state of a system(at least if one considers the

system by itself,ignoring any quantum correlations it may have with other systems). In this latter sense,if one knows the actual density matrix(not just an estimate based on additional uncertainty about the actual statistical state of the system), one has complete information about the system in whatever statistical state it is actually in.However,it is in the former sense,of how much information is possible about the system(which depends on the actual statistical state rather than on how well that is known),that one says that the evolution of a pure state to a mixed state by Hawking’s proposed Eq.1for black hole formation and evaporation would be a loss of information.A measure of the possible amount of information in a system with Hilbert-space dimension m and statistical stateρis

I=S max?S=ln m+T r(ρlnρ).(2)

This loss of information does not necessarily mean that a knowledge of the?nal mixed state would be insu?cient to reconstruct the initial state.(The?nal mixed state could in principle be learned to arbitrarily high statistical accuracy from the results of repeated measurements of a su?ciently large set of observables if one had a su?ciently large ensemble of systems with that same mixed state.)To illustrate this claim and the points made above,consider a spin-1/2system,so that the indices a,b,c,d range from1to2.The general statistical state of the system can be written as

ρ=ρ11|↑ ↑|+ρ12|↑ ↓|+ρ21|↓ ↑|+ρ22|↓ ↓|,(3)

whereρ11andρ22must be nonnegative real numbers that sum to unity andρ12and ρ21must be complex conjugates withρ12ρ21≤ρ11ρ22in order thatρbe a positive-semide?nite Hermitian unit-trace operator.This statistical state can be charac-terized by the polarization vector P with Cartesian components(ρ12+ρ21,iρ12?iρ21,ρ11?ρ22)and gives a probability(1+P)/2,where P is the magnitude of P,of ?nding the spin in the direction of P.

Now an example of a superscattering matrix for this system is

1

$cd ab=λδc aδd b+

Cartesian components of the spin for a large ensemble of systems with this identical ?nal state)would readily give the initial state,simply by dividing the polarization vector byλ.(Of course,I am always assuming that the law of evolution,in this case parametrized byλ,has already been determined,as it could have been by measuring the results of the evolution of an ensemble of systems in di?erent initial states.)Only in the special caseλ=0does the?nal statistical state not uniquely determine the initial statistical state.

Although the simple case just given is quite special,the property appears to be generic,that a superscattering matrix is invertible within the restricted set of density matrices comprising its range,if the dimensions of both the initial and?nal Hilbert spaces are the same?nite integer m.That is,for the set of(m2?1)2real parameters de?ning the generic superscattering matrix,all but a set of measure zero,given by one or more hypersurfaces of codimension one,or dimension m2(m2?2),in the (m2?1)2-dimensional space of all the parameters,gives an invertible$.Of course, if$increases the entropy S and decreases T rρ2,there are hypothetical positive-semide?nite?nal density matrices(e.g.,pure states)that have no pre-images by$ in the space of positive-semide?nite initial density matrices.(The inverse of$would map them to matrices with one or more negative eigenvalues.)However,the generic $would have an inverse within the smaller set of?nal density matrices given by the range of$acting on the set of general positive-semide?nite initial density matrices of the same?nite dimension.On the other hand,if the dimension of the?nal Hilbert space were smaller than that of the initial one(a rather violent violation of CP T), no superscattering matrix could be invertible.

Thus one might say that a nonunitary superscattering operator does not generally lead to an absolute loss of information about the initial state,assuming the Hilbert spaces stay the same?nite dimensions.However,it does lead to a degradation of partial information in the sense that the empirical accuracy of the measured state is reduced in extrapolating back(e.g.,in dividing the?nal approximately-determined polarization vector byλ).Nevertheless,I shall continue to follow the usual convention of de?ning a loss of information as an increase in the?ne-grained entropy S≡?T r(ρlnρ)of the complete system.

This loss of information proposed by Hawking would be a new feature of quan-tum gravity,not seen in other quantum?eld theories in a?xed globally hyperbolic spacetime.Gibbons[6]speculated that it might be related to the inde?niteness of the Einstein action of general relativity for positive-de?nite metrics(Riemannian or ‘Euclidean’as opposed to pseudo-Riemannian or Lorentzian).

2.Initial Objections and Alternatives to Hawking’s Proposal

To the best of my knowledge,the?rst objection to Hawking’s proposal of a loss of information was made by the referee[7],who apparently forced Hawking to change the title from“Breakdown of Physics...”to“Breakdown of Predictabil-ity....”However,I am not aware of whatever detailed objections he may have given.So far as I know now,the?rst published objection was given by Zel’dovich [8],who asked whether Hawking’s“very radical”conclusion is“connected with the fact that he considers a macroscopic black hole?...Could not this new and greater indeterminacy arise as a result of this macroscopic and semiclassical treatment of the situation?...Must one not treat the emission of a black hole at the quantum level?Can one not,and should one not formulate the theory with black holes in such a way that additional indeterminacy and incoherence do not arise?”

Unaware of Zel’dovich’s objection,I independently objected to Hawking’s pro-posed nonunitary evolution Eq.(1)on the grounds that it is not CP T invariant, since it takes pure states to mixed states,but it does not give the CP T-reversed process of mixed states going to pure states[9].After making that new observation, I raised the same objection that Zel’dovich had[8],that Hawking’s proposal was based on the semiclassical approximation(SCA).I explicitly showed how the SCA would be expected to break down in a noticeable way from?uctuations of the black hole momentum,long before the black hole shrunk to the Planck size,if momentum is conserved in detail and not just on average.Although this particular?uctua-tion e?ect by itself would not help restore any of the information Hawking believed would be lost,it did at least illustrate the uncertainty of relying on the SCA for the question of whether the results of black hole evaporation are predictable in the sense that a pure quantum state would be.Therefore,I listed a number of open possibilities that occurred to me at that time,which it may be useful for me to rewrite and comment on as I see them today:

(A)Evolution by an S matrix.This would say that in a quantum theory of ev-erything,including the gravity of the black hole,a pure state of the complete system would always go to a pure state,and no information would be lost.At the time,I wrote that“in the absence of further information,it would seem most productive to pursue the most conservative possibility(A).”Today I might be somewhat inclined to delete the word“most,”but I have not yet seen any strong evidence that(A)does not remain an open possibility,for reasons I shall partially discuss below.In some sense it would be the simplest possibility,though I must admit I still have little idea how it might be actually realized and yet be consistent with what we think we know

about gravity.More recent arguments for this viewpoint include[10-49],as will be discussed below.

(B)Evolution by a CP T-noninvariant superscattering matrix.This was Hawk-ing’s proposal[5].It seemed undesirable to me to believe in a violation of CP T invariance,despite the previous arguments of Penrose[50],but Hawking,though not one to believe Penrose’s arguments on this,concurred[51]with Wald[52-54] that it would be enough to have CP T in the weak form of CP T-invariant transition probabilities

p(c→a)≡$cc aa=p(Θa→Θc)(5)

between an initial pure state c and a?nal pure state a(no sum on these repeated indices),by using Eq.1as an intermediate tool but not interpreting the?nal density matrix given there as literally the actual?nal state of the system.I have found this hard to swallow in my na¨?vely realist view of density matrices as being the more basic objects,and of probabilities as being derived from them,rather than the other way around.However,Hawking’s argument[55]that one should interpret Eq.1as merely an intermediate tool for calculating conditional probabilities(given a measurement of a particular initial pure state,what is the conditional probability of measuring a particular?nal pure state?)now makes more sense to me[56].Then the asymmetry may indeed be more in the conditional nature of the probability than in any time asymmetry(e.g.,CP T noninvariance).

(C)Evolution backward in time by a CP T-noninvariant superscattering ma-trix.I threw this in as a counterpoint to(B)and wrote,“Then the past would be predictable from the future,but the future would not be predictable from the past.This possibility would suit historians better than physicists.”I suppose that if the superscattering matrix were merely used to calculate conditional probabilities, and if(B)were applicable when the condition were to the past of the result whose conditional probability were to be calculated,then(C)would apply whenever the result were to the past of the condition.This indeed appears to be roughly the case when historians ask,“What is the probability that x happened in the past,given our present records?”

(D)Evolution by a superscattering matrix which is not of the form Hawking proposed,i.e.,not

$cd ab=S c aAˉS d bA,(6)

where A denotes an orthonormal basis of states(to be summed over)of the“Hilbert space of all possible data on the hidden surface”which is to surround“either singu-larities(as in the Schwarzschild solution)or‘wormholes’leading to other space-time

regions about which the observer has no knowledge(as in the Reissner-Nordstr¨o m or other solutions)”[5].S c aA would be an S-matrix from a state c on an initial surface (before a black hole formed)to a state aA with a on a?nal surface(after the black hole evaporated)and A on the hidden surface.In my Letter I explicitly assumed an $with this form in(B),and also in(C),except with“initial”and“?nal”reversed in(C).I didn’t have any motivation for considering other forms of a possible super-scattering matrix,which would be of no help in avoiding violating CP T invariance in my strong sense.However,it now appears to be necessary if the initial and?nal Hilbert spaces have the same?nite dimension(see below).

(E)Evolution of density matrices deterministically but nonlinearly.I don’t see any clear motivation for this,but why not leave it on the table as an open possibility? Nonlinear generalizations of the quantum mechanical evolution of pure states have been considered[57-60],but I am not aware of much discussion of nonlinear evolution of density matrices that do not keep pure states pure[61].The apparent linearity of quantum mechanics seems to me to be the main reason why we do not notice any in?uence from other Everett worlds,which surely must exist unless quantum mechanics is modi?ed in a very particularly nonlinear way(e.g.,by the collapse of the wavefunction somehow very precisely into just the quasiclassical components we observe).I would think that any proposed nonlinearities of quantum mechanics would be very strongly limited by our nonobservance of such other-worldly e?ects.

(F)Evolution in which black holes or naked singularities form but do not disap-pear.These would now be called remnants or various other terms[62-65],but this term is also taken to mean other massive objects that I did not think to consider

[66],and also objects that can decay unitarily after a very long time[67,68],which

I would have counted as an intermediate state in possibility(A)but did not con-sider explicitly.As far as the absolutely stable remnants go,I uncritically accepted Hawking’s argument that“Because black holes can form when there was no black hole present beforehand,CP T implies that they must also be able to evaporate com-pletely;they cannot stabilize at the Planck mass,as has been suggested by some observers”[5,69].However,Horowitz[70]led me to realize that the only require-ment from CP T is that a CP T-reversed remnant should be able to combine with CP T-reversed Hawking radiation to form a large CP T-reversed black hole(i.e.,a white hole)which can convert into the CP T reverse of whatever collapsed to form the original black hole;if there is no CP T-reversed Hawking radiation impinging on the CP T-reversed remnant,it can be absolutely stable and yet be consistent with CP T invariance.

It would seem that there could be several possibilities for a set of absolutely

stable(when isolated)remnants resulting from black hole evaporation that would be consistent with CP T:(1)The set could be empty.Then stable remnants would not exist.(2)The set could be nonempty and include the CP T reverse of every element of the set(or at least a quantum superposition thereof).Then each remnant could in principle be made to go away by combining it with the CP T reverse of the Hawking radiation that accompanies the formation of the CP T-reversed remnant.(3)The set of remnants could be nonempty but distinct from the CP T-reversed set of anti-remnants.(For example,they could be cornucopia geometries[62-65]with internal regions that are expanding toward internal future null or timelike in?nities,whereas anti-remnants would have internal regions contracting from internal past null or timelike in?nities.)Then remnants could never be destroyed(as anti-remnants could by the CP T reverse of the process of remnant formation),although presumably they could merge or be swallowed by black holes(which could later become remnants again).

In this latter possibility,it is presumably true[69,71]that a?xed?nite energy in a box would never evolve into an absolutely CP T-invariant thermal state,since there would eventually tend to be more remnants than anti-remnants.However, contrary to[69,71],I see nothing violating CP T-invariant evolution in this scenario. Furthermore,if from the outside remnants don’t look much di?erent from anti-remnants(as would be the case for cornucopia that tend toward static con?gurations as seen from the outside),the state of the box at late times could appear very nearly CP T invariant,particularly since one can readily estimate that it would be exponentially rare to have more than one remnant in the box(assuming they can merge or fall into a black hole).

Possibility(3)might be subdivided into case(a)in which information could never be retrieved from inside the remnants,case(b)in which some,but not all, of the information could in principle be retrieved,and case(c)in which all of the information could in principle be retrieved.In case(a)all of the remnants presum-ably would be distinct from anti-remnants,in(b)some,but not all,of the remnants would be,and in(c)apparently there would be only a single remnant state that would be distinct from its CP T-reversed anti-remnant.Cornucopia with internal future null or timelike in?nities,where information can go and never be retrieved, would presumably fall into case(a),unless some of the internal information does not go to the future null or timelike in?nity,in which case they might fall into case (b).

(G)Evolution in which the disappearance of black holes results in mixed states that are unpredictable.At the time,I did not have any proposed model for this,

but later I realized[72,73]it could occur for a CP T-invariant model in which our universe is an open system,and information can both leave and enter.An analogue would be a room with a window:from the density matrix of the inside of the room alone at one time,one cannot know what light might come in from the outside,and hence one cannot predict even the density matrix inside the room at a later time.Unlike the case of deterministic evolution of the density matrix by a generic superscattering matrix,in the case of an open system one generally cannot extrapolate backward from the later density matrix to a unique earlier one, so information would be truly lost in an even more fundamental way.

(H)Replacement of density matrices by something more fundamental.I had no proposals for this,but in the Letter I did say,“In view of the historical developments in the concept of nature,one might say that the most radical,(H),is the most re-alistic.”The interpretation of taking the superscattering matrix as merely being a tool to calculate conditional probabilities would in some sense require this,so per-haps Hawking’s proposal of information loss would?t better here than under(B). It is now also extremely interesting to see a whole new formal approach being de-veloped,the decoherent histories reformulation of quantum mechanics,particularly the generalized quantum mechanics without states[74-78].If it is indeed the correct approach,it should have something to tell us about black holes and information.

In the debate I thus initiated with Hawking,informal discussions showed me that relativists tended to side with Hawking’s viewpoint,often arguing that the event horizon should be an absolute barrier to the recovery of information,whereas particle physicists were much more sympathetic to the possibility of a unitary S-matrix.For example,Witten[79]dismissed the idea of the horizon as a barrier,since the uncertainty principle applied to gravity would prevent its localization.However, in the early years there were very few papers about the subject.

One interesting earlier paper that was never even published was Dyson’s sugges-tion that if information were lost from our universe,it might simply go into what we would now call a baby universe rather than being destroyed at a singularity [80].(Around the same time,Zel’dovich[81]suggested that baryons could leave our universe and go into a closed space by the Hawking process,but he did not discuss information there,and,as noted above,he later argued[8]against Hawking’s pro-posed loss of information.)I have already cited Wald’s papers[52-54]that argued that CP T should indeed be broken in a strong sense and pointed out how it could be preserved in a weak sense by a superscattering operator.

A conference abstract of mine[10]noted that another problem with the semi-classical approximation is that if one feeds a black hole for a su?ciently long time

at the Hawking emission rate,the SCA gives an arbitrarily large number of internal con?gurations for a black hole of a given size,not just the exponential of the entropy Hawking had derived for it[2,82].Furthermore,it seemed to me that even without CP T invariance in the strong sense,it would be most natural to assume that the Hilbert spaces on the initial and?nal surfaces would have the same dimension,and then(at least if those dimensions were?nite)the postulated existence of the3-index S matrix of Eq.6would imply that the hidden hypersurface could only have a trivial Hilbert space(one unique state A).Then the sum over A in Eq.6would collapse to a single term,giving a unitary superscattering matrix.

The lack of CP T invariance in the strong sense for a superscattering operator and the problem with the dimensions of the Hilbert spaces motivated me to consider the example of possibility(G),that our universe is an open system,with not one but two hidden Hilbert spaces,one from which states can come(say baby universes in the past),and one to which states can go(say baby universes in the future)[72,73]. One could postulate that there is an S matrix,from the product Hilbert space of our past universe and the past baby universes,to the product Hilbert space of our future universe and the future baby universes.If the initial density matrix on the past product Hilbert space were a tensor product of a?xed density matrix for the past baby universes and an arbitrary density matrix for our past universe(so the baby universes started uncorrelated with our universe),then the?nal density matrix of our universe would indeed be given by a superscattering matrix(depending on the initial baby universe density matrix,but that is assumed?xed)acting on the initial density matrix of our universe,which would be possibility(B).This would be like the case of a room with a pure state outside,say the completely dark vacuum state, or perhaps a?xed thermal state which is completely uncorrelated with what is in the room.In this case,from knowing the initial state of what is inside,one can give the density matrix of what will bounce back from or enter the window.At the other extreme,if the?nal density matrix on the future product Hilbert space were a tensor product with a?xed density matrix for the future baby universes,then there would be evolution backward in time by a reversed superscattering matrix,possibility(C). But in general,if the baby universes are correlated with our universe in both the past and the future,or if their statistical state is unknown,one would not have a superscattering matrix at all,possibility(G).

This possibility in some sense sounds the most likely,especially if quantum grav-ity can allow connections to baby universes that can branch o?or join on.However, it raises some questions that are not yet very clear.For example,if the dimension of the Hilbert space of our universe stays the same from past to future,then the two

hidden Hilbert spaces should also have the same dimension in order that there be an S matrix between the two product Hilbert spaces(at least the argument would be valid if all these dimensions were?nite).That would mean that there would be in principle as many ways for information to enter our universe as to leave it.And yet the semiclassical approximation seems to show many ways for old information to leave our universe(e.g.,by going down a black hole),but the only place it seems to allow for new information to enter is at a possible naked singularity at the end of the black hole evaporation,where the semiclassical approximation breaks down. One might even expect quantum gravity to heal the naked singularity so that no new information enters the universe from it,a possibility I termed Quantum Cosmic Censorship[9].In other words,the semiclassical approximation suggests that the dimension of the future hidden Hilbert space is large,but that the dimension of the past hidden Hilbert space is small or perhaps even zero.If the two are actually equal,which suggestion is correct?Taking the large dimension supports the view that pure states go to mixed states,but taking the small dimension suggests that little or no information is lost,and that pure states may stay pure.This is one of the strongest reasons for me to think that possibility(A),unitary evolution,is at least reasonably likely,and to resist what often seem to me to be premature reasons to dismiss it.

On the other hand,it could turn out that even if the dimensions of the two hidden Hilbert spaces are identical and nontrivial,some principle in?uencing the states on those two spaces might make it so that in actuality more information leaves our universe than enters it.This is apparently happening in my o?ce room now at night as I type this,for outside it is dark,and little information in the visual band of photon modes is coming in,whereas there is much more information going out from the light inside.From the inside,I can more easily predict the light I now see(re?ected)in the window,whereas in the daytime,I cannot predict the light entering from the clouds outside I see?oating past.So in this language the question would be,why do past baby universes seem to be dark?

Perhaps the answer is that something like the Hartle-Hawking no-boundary pro-posal[83-86],the Vilenkin tunneling proposal[87-94],or the Linde in?ationary pro-posal[95-98]makes the state of small past baby universes simple,just as the state of our past universe seems to have been simple when it was small.Now our universe has grown to be large and complicated,and so if it connects to the Hilbert space of small baby universes in initially simple states,information would naturally tend to go from our universe into the baby universes rather than the other way around.

It would be interesting to try to formulate the problem of black hole information

in terms of the no-boundary proposal,at least if one could avoid being stymied with all of the problems of the path integral for gravity.Assuming that the path integrals are over some contours of complex geometries,one would have to reformulate the concepts of“initial”and“?nal,”“past”and“future,”etc.so that they are not in terms of the classical Lorentzian concept of time.And then there is the question of whether it is better to treat the possible“loss”of information as a process to be seen in a decohering set of histories[99-103,74-78,104],or as something to be found in the records existing in a single“marvelous moment”[105-122].An interesting recent paper by Smolin[123]takes a quantum-cosmological approach to the problem and conjectures that if quantum e?ects do not eliminate singularities,“loss of information is a likely result because the physical operator algebra that corresponds to measurements made at late times must be incomplete.”

3.Further Arguments for Four-Dimensional Black Holes

After these rather few responses to Hawking’s original proposal for information loss,some new interest was generated by a new paper[55]in which Hawking at-tempted to put the idea in an axiomatic framework and apply it to processes involv-ing tiny virtual black holes.He proposed a set of axioms for scattering in quantum gravity with asymptotically?at boundary conditions.These included most of the usual axioms but omitted the axiom of asymptotic completeness,so that a pure ini-tial state would not give a unique pure?nal state.Alvarez-Gaum′e and Gomez[12] gave a rigorous derivation of CP T from Hawking’s axioms and pointed out some dif-?culties with Hawking’s idea of asymptotic incompleteness.Gross[13]showed that nontrivial topologies in the path integral for quantum gravity need not give asymp-totic incompleteness and a loss of information,though Hawking[124]argued that more complicated examples than the ones Gross considered would.Ellis,Hagelin, Nanopoulos,and Srednicki[14]noted that with a superscattering matrix rather than an S matrix,symmetries no longer imply the usual conservation laws,so that the latter would need to added independently.Banks,Peskin,and Susskind[15]showed that making the superscattering operator act locally would lead to a violation of energy-momentum conservation.Hawking’s response[124]was that it should not be made into a local operator.More recent studies[29,33]have rea?rmed and intensi?ed various aspects of this problem but do not seem to have conclusively shown that no formulation with loss of information could be consistent with energy-momentum conservation.

In addition to the proposals for loss of information,and the ensuing counterargu-

ments,a program on the other side,pursuing possibility(A)above,was launched by ’t Hooft[16,21-23,25-28,31].He made a bold analogy between string worldsheets and event horizons and attempted to work out the principles for an S-matrix for black hole processes.This has provided some innovative ideas of how information might be preserved,but it is unfortunately probably too optimistic to expect this program to be brought to completion in the foreseeable future,because of the severe di?culties of quantum gravity.

Another development that appeared to tip the balance somewhat toward pos-sibility(A)is the work on quantum wormholes and baby universes[125-127,11, 128-138,112,139-146].This primarily addressed the question of the cosmological constant,but it also addressed the question of whether information can get lost into wormholes.The somewhat surprising answer was that although there may be di?erent superselection sectors of the theory(each with di?erent low-energy e?ec-tive coupling constants that would have to be determined experimentally rather than theoretically from some fundamental‘theory of everything’),in each sector one would get an S matrix with no loss of information(though Strominger has recently argued[147]that in each sector one would get an$matrix).Few of the experts claimed that black hole formation and evaporation could be described by wormholes,but Hawking did[133],which seemed to undermine his proposal for loss of information.He did try to argue that the uncertainty of the coupling constants represented the loss of information[138,145].However,it would really be di?erent from his previous proposal,in that once one did enough repeated black hole collapse and evaporation experiments to measure the relevant e?ective coupling constants (assuming there were only a?nite number that had any signi?cance for the process at hand),one could predict?nal pure states for any subsequent experimants.An interesting question would be the number of relevant e?ective coupling constants for a certain process,and only in?nity would correspond to the continual uncertainty of Hawking’s original proposal.

To illustrate this di?erence,consider a simpli?ed process in which there is a?nite box containing either a“red”or a“green”particle of the same mass,each of which would be absolutely stable in the absence of gravity.With gravity,suppose each could collapse to form a black hole which could then emit either kind of particle.(If you do not believe one particle could do this,replace it by two particles or whatever you think the minimum number is.)For simplicity,assume that the black hole can emit its energy in no other forms.In Hawking’s original proposal,an initial pure state of red,say,would become mixed and would tend toward the mixture of 50%probability for red(but never lower)and50%for green(but never higher).

However,in the wormhole analysis,there would presumably be an e?ective coupling constant for the transition rate from red to green and vice versa,leading to a coherent oscillation between red and green in each superselection sector.A priori,one might not know this rate and therefore not be able to predict better than a density matrix for the?nal state.However,after su?cient measurements of the rate to?nd out which superselection sector one is in,one could predict thereafter the oscillation rate.In particular,one could predict times at which the originally red particle has a probability of unity to be green(to the accuracy of the measured coupling constant), a situation that would never occur for Hawking’s superscattering matrix.

Here I have been assuming that there is only one relevant coupling constant for the transition rate.Of course,there might be more,say depending on the state of the particle in the box.If there were were an in?nite number of relevant coupling constants,and if they coupled to states outside the box(as they presumably would have to if there are only a?nite number of relevant possible states within the box), then one might never be able to predict a probability greater than50%for a green particle.This might happen,for example,if the coupling were su?ciently strong to the records of the previous measurements so that they become anti-self-full?lling prophecies:the results of repeated experiments would be identical only if there were no records to mess up the subsequent experiments,but if no records were kept,then no one could predict the repetition.

At one time I thought Hawking’s suggestion of describing black hole formation and evaporation by a wormhole process was reasonable,and then it seemed that there would be no loss of information once enough measurements were made(with various speculations of how many might be needed)[148].However,it now seems to me that the standard wormhole calculus is probably not applicable[149],since it involves integrating over length scales up to the wormhole length in order to get an e?ective theory at larger scales.With black hole formation and evaporation that would take a timescale of order M3in Planck units(assuming no long-lived remnant at the end,which would only intensify the problem),it would seem that one would need to integrate over length scales up to about M3,and the e?ective theory would apply only on length scales larger than that.But then the e?ective theory could not describe what collapsed to form the hole(in a much shorter time)or the individual quanta being emitted(with wavelength of order M).

Bekenstein has recently conjectured[32]that since Hawking radiation is not pre-cisely blackbody but rather is greybody(because of the partially re?ecting curvature and angular momentum barriers around a black hole),this nonthermal aspect could code the information in the black hole.However,it does not seem that this e?ect,

or another similar nonthermal e?ect(such as stimulated emission when incident radiation is present[36]),could by itself ever lead to a pure?nal state[150,151], since each of them occurs already in the semiclassical or even classical approxima-tion.Indeed,the generalized second law for quasistationary black holes[152-155, 1,2,156-184]implies that under these approximations the entropy of the radiation would always be at least as large as one quarter the area lost by the black hole. The information actually in the radiation simply means that it is not completely random.For example,it might be such that from the complete?nal state,even if it is an impure density matrix,one could in principle deduce the complete initial (possibly pure)state,as was discussed above.However,this does not exclude the possibility that the information in the sense of Eq.(2)above might decrease.

Another attempt to avoid a loss of information in black holes is to postulate that black holes never really form.For example,Frolov and Vilkovisky[185,186]and H′a j′??c ek[17,20]conjectured that gravitational collapse might lead to no singularities or event horizons(only apparent horizons),and so no true black holes.Nevertheless, there would be a very large time delay before ingoing null rays become outgoing null rays,and there would be Hawking radiation,so the quantum-corrected system would appear much like a true semiclassical black hole,thus ful?lling the correspondence principle.Unfortunately,our understanding of quantum gravity is too meagre at present to con?rm or refute this conjecture,at least in four dimensions.

An even more direct way to try to eliminate black holes is to assume a di?erent classical theory of gravity.For example,Mo?at[187,188]has postulated that if the correct theory of gravity were NGT rather than GRT,the NGT charge could prevent black holes from forming.But even if NGT were a consistent theory of gravity[189-193],it would allow black holes to be formed from pure radiation without NGT charge,and so it would not really succeed in circumventing the problem.It would probably be very di?cult for any simple consistent classical theory of gravity(which agrees with Newtonian gravity and with special relativity in the appropriate limits) to avoid producing black holes in all circumstances.

Other arguments have been given[194-197]that black holes have their area A quantized in units of CL2P l,where L P l is the Planck length(set equal to unity), and C is a numerical constant of order unity(e.g.,8π[194],4ln2[195,196],or 16/(3π)[197].This quantization of the black hole would seem to make most sense if there were unitary evolution,with the black hole as part of the intermediate quantum state,and with no loss of information.However,these proposals appear to imply[195]that an uncharged black hole with zero angular momentum and mass M?1(which has an area A=16πM2,at least classically)would have the

nearest di?erent energy level di?ering by an energy very nearly C/(32πM).Then the black hole could absorb or emit single quanta of radiation with energies only integer multiples of this(i.e.,wavelengths equal to64π2M/C,which is of the order of the Schwarzschild radius2M of the hole,divided by an integer,for radiation quanta of zero rest mass).This line spectrum[195]would be signi?cantly di?erent from the expected semiclassical limit in which one gets quantum?eld theory in the classical spacetime of the black hole,which would allow absorption or emission of a continua of frequencies or wavelengths(e.g.,wavelengths longer than64π2M/C).

A loophole in this argument is the possibility that the classical relation between area and mass is invalid,so that an area quantization does not imply the na¨?vely corresponding mass quantization.But in any case,if the black hole mass is quan-tized,I would expect the levels generally to be discrete and be separated,on average, by the inverse of the level density(e.g.,by roughly e?A/4,or e?4πM2for uncharged black holes with zero angular momentum),rather than being clumped in highly degenerate levels that are much further separated(e.g.,by C/(32πM)).(Actually, I would expect the levels to be discrete only in the case that one put the black hole in a?nite box and considered the energy levels of the entire system in the box,e.g.,the black hole plus the surrounding radiation.For a black hole in in?nite space,the instability to evaporation would smear out the levels by amounts much greater than their separations if the separations were indeed of order e?A/4.)If my expectation were true,it would seem quite possible to get,in the semiclassical limit, ordinary quantum?eld theory in the curved spacetime of a classical black hole,with no noticeable line spectra or departures from the expected ordinary thermal spectra.

There has also been a long sequence of analyses of black hole evaporation in string theory,and related processes,by Ellis,Mavromatos,and Nanopoulos[198-210].The latest conclusion seems to be[210]that there is an$matrix with loss of information.However,I am not competent to judge this work,and there doesn’t seem to be much other comment on it in the literature that I am aware of.

4.Two-Dimensional Black Hole Models

After nearly sixteen years in which only a few papers per year were written directly about Hawking’s proposal,the subject experienced a strong upsurge of in-terest as a result of a paper by Callen,Giddings,Harvey,and Strominger[211].This paper replaced the presently intractable problem of four-dimensional gravity with a two-dimensional model theory,motivated by extreme dilatonic black holes[212,213] and by string black holes[214-218].This two-dimensional model is much simpler

and yet seems to capture many of the aspects of four-dimensional gravitational col-lapse and evaporation.One might object that this toy model might miss the heart of the problem in four dimensions,but since we do not yet have any consistent understandable theory of quantum gravity in four dimensions,any attempt to un-derstand the problem must make some simpli?cation or truncation of the unknown complete theory,and so one might as well start?rst with the simplest such model that apparently has enough of the realistic features.Although the two-dimensional model does not really have independent gravitational degrees of freedom,it does have black holes and matter degrees of freedom(the dilaton and minimally coupled scalars),which can give Hawking radiation and lead to at least some measure of black hole evaporation when the back reaction of this radiation is included.

This simpli?ed model can be solved exactly classically.However,its extension to a consistent quantum theory appears to have an in?nite number of arbitrary parameters[219-236,30,237-247,46].In some cases the quantum theory may be be solved exactly,and in a wider class of cases the semiclassical equations are analytically soluble,but no completely satisfactory quantum model has been yet found.Much of the work has concentrated on solving the semiclassical equations of the original CGHS[211]model.At?rst it was thought[211]that there would be nonsingular evolution with an S matrix,but then it was shown[62,220,248-254] that the semiclassical equations generally lead to singularities.It is not yet known what this model,or the various modi?cations of it that have been proposed,would really give in a full quantum analysis concerning information loss.However,this model has inspired much new thought about the subject,some of which I shall now summarize.

One approach,which is somewhat motivated by and patterned after’t Hooft’s program[16,21-23,25-28,31]in four dimensions,is to look for a unitary S-matrix for two-dimensional black hole formation and evaporation[30,34,37,45,46].This can apparently be done,for example[34,37],by imposing re?ecting boundary conditions at a critical value of the dilaton?eld,though there are some subtleties(e.g.,when this critical value occurs on a spacelike line),and of course there is the question of whether these boundary conditions are realistic.However,it is interesting that this work seems to give an explicit example of a process that looks very much like black hole formation,followed by nearly thermal Hawking radiation,and yet is described by an S-matrix with no loss of information,possibility(A),that I have continually argued has remained a viable alternative.Unfortunately,it appears that the full S-matrix of[34,37]may not be unitary,and the part that is may merely represent the part in which no black hole forms[255].

A second series of papers patterned after’t Hooft’s program is[38,47,49], which proposes that there is a“stretched horizon,”a membrane just outside the global event horizon which appears to be physically real to an outside observer. From the outside viewpoint,“the stretched horizon is a boundary surface equipped with microphysical degrees of freedom that appear in the quantum Hamiltonian used to describe the observable world.”As a quantum object,the stretched horizon may be able to store and return all of the information of the gravitational collapse to the outside.

It is not clear in this approach how the information gets from the infalling?elds to the stretched horizon.It is not proposed that an infalling observer would feel his or her information getting bleached,so that it would all immediately go onto the stretched horizon as he or she crosses it.Instead,the claim is that“there is complementarity between observations made by infalling observers who cross the event horizon and those made by distant observers.”Preskill’s view of this[256, 255]is that any apparent contradiction which arises when one tries to combine the viewpoints of infalling and outside observers will actually involve assumptions about physics at energies above the Planck scale[49].Nevertheless,it would be useful to have a mechanism for seeing how in detail the information can get onto the stretched horizon.

Another approach,which lends some support for the opposite conclusion,is the study of scattering by extremal black holes[257,211,258,62,259-261,63,64,262, 263,65].It does seem from these analyses that if one had a theory with absolutely stable large extremal black holes(e.g.,electrically charged holes in a theory with no charged particles,such as Einstein-Maxwell theory with only neutral other?elds, or magnetically charged holes in a theory with no magnetic monopoles),then there may well be an in?nite number of arbitrarily low-energy perturbation states deep down in the throat of these black holes.One could presumably lose an arbitrary amount of information into these states,though it would be a bit ambiguous whether one said this information were lost from our universe or persisting in the remnant.

To be relevant to the problem of black hole formation and evaporation,one would have to assume that these stable black holes are not merely eternal parts of a background spacetime but can be produced by some process.If the black holes are charged in a theory with no charged matter,one could not form them from the gravitational collapse of matter.One might instead imagine forming them by pair production.This raises the problem that if there are an in?nitely large number of these remnant states below a?xed?nite energy,then it would appear that they should be produced at an in?nite rate[67](e.g.,in the Hawking radiation of a larger

black hole).This has appeared to be a very strong argument against an arbitrary amount of information from gravitational collapse going into a remnant of bounded mass(e.g.,the Planck mass).

However,possible reasons have been given why the standard argument might be wrong and that an in?nite degeneracy of remnants can be produced at a merely ?nite rate.The?rst reason given[67]was that the remnant form factors might vanish when the momentum transfer is timelike.This possibility,which I am not competent to judge,seems to have been generally ignored in the literature.Another reason given is that the remnants may have in?nite internal volumes which can carry an arbitrarily large amount of information while being pair produced at a ?nite rate[63,64,262,65].On the other hand,there are counterarguments[263] that unless there is what would be described from the e?ective remnant theory as a “strong coupling conspiracy,”there would still be an in?nite production rate.The possibility of an arbitrary amount of information remaining in remnants seems to be more open than I would have thought it was two years ago,but it is yet by no means convincing to me.

Another remnant scenario is Giddings’proposal[66]that the information from gravitational collapse ends up in a remnant whose mass and size depend on its information content.This would avoid the problem of in?nite production,since there would only be a?nite number of states up to any given mass(in a?nite volume),and so any process with a?nite amount of energy available could only access a?nite number of states.However,even Giddings recognizes that these remnants“would seem to require new physics at weak curvatures and runs afoul of causality”[263].

Bekenstein[183]has raised a related objection to information-bearing remnants based on his conjectured limit[158]on the entropy S of a system of bounded linear size R and energy E,S≤2πRE.(This conjecture is supported by a number of examples in?at spacetime[158,162,165,264-266,173]if one chooses judicious de?nitions for S,R,and E,and it has somewhat weaker support[159,175-177, 181]for self-gravitating systems,but it by no means seems to be proved in general [160,267,161,166].)If the thermodynamic entropy S of a remnant is indeed limited,but if the information capacity(the number of possible internal states)is not limited,one would have the same problem[10]discussed above for the semiclassical approximation applied to black holes of?nite thermodynamic entropy that are fed radiation for a su?ciently long time at the Hawking emission rate.However,if those who believe an arbitrarily large amount of information can be put into a black hole in this way without an equal amount coming back out have an answer for this

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◆促使学生进行思考 2.1.5 预警系统 ◆当学生未能达到教师设定的标准时，系统自动向学生发出警示 ◆可创建多种规则 2.1.6 测验和调查 ◆17种可选择的题型 ◆可设置是否允许多次尝试 ◆可进行时间控制 2.1.7 成绩中心 ◆直接编辑成绩 ◆添加外部成绩 ◆加权计算成绩 ◆智能视图 ◆生成成绩报告 ◆发送成绩报告 2.1.8 学业表现统计 ◆及时了解学生的学习情况 ◆学生参与网络学习的数据 ◆学生各个课程内容的学习情况 2.1.9 支持协作活动的平台 ◆讨论板 ◆邮件、消息 ◆虚拟课堂、聊天室 ◆工作流程流程化的协作活动管理可查看流程进展情况 2.1.10 自评与互评 ◆促进学生更好地理解评分标准 ◆促进学生之间的建设性反馈 ◆完全客观的反馈（可选匿名评估）

Blackboard在线教学管理系统

Blackboard在线教学管理系统 Blackboard是一个由美国Blackboard公司开发的数位教学平台，被广泛认为是业界领先的课程主导型管理系统。数位教学意指数字化教学，老师和学生可以在多媒体、网络组成的平台内进行各种课程方面的交流。Blackboard在线教学管理系统，正是以课程为中心集成网络“教”“学”的环境。教师可以在平台上开设网络课程，学习者可以自主选择要学习的课程并自主进行课程内容学习。不同学习者之间以及教师和学习者之间可以根据教、学的需要进行讨论、交流。“Blackboard”为教师、学生提供了强大的施教和学习的网上虚拟环境，成为师生沟通的桥梁。 欧桥国际学院（ObridgeAcademy）就是采用最领先的在线教育管理系统–“Blackboard Learning System” 平台以课程为核心，每一个课程都具备以下4个独立的功能模块： ●教学组织管理–方便地发布和管理教学内容、组织教学活动 ●交流互动工具–支持异步和同步的交流协作 ●考核管理功能–自测、测验、考试、调查和成绩统计管理 ●管理统计功能–课程以及平台的管理和统计 登陆平台的三类身份：系统管理员、教师、学生。 系统管理员：个性化定制平台界面风格、功能；根据学校的根据实际情况设定、添加、管理用户；统计并管理整个平台的使用情况；为其他校园信息化的应用系

统提供服务和接口等。 教师：管理教学、编辑组织教学内容、在线考试、批改作业、组织在线答疑、统计分析学生学习情况等。 学生：选修课程、安排学习计划、查看课程内容、提交作业、参加在线测试、查看学习成绩、协作学习和交流、参与学校社团交流等。 Blackboard教学管理平台是目前市场上唯一支持百万级用户的教学平台，能使学校更好地进行课业交流，达到自主学习、教学相长的目的。使任何教师、学生和研究者都可以随时随地浏览内容、获取资源、评估教学效果、实现彼此的协作。可帮助教师在线授课、测验、检查作业,学生可以通过各种论坛区与师生交流，巩固学习效果，增进学习兴趣。Blackboard界面直观，工具简单易用，对技术人员依赖程度低。通过与世界最大的网络教学平台提供商Blackboard的合作，还可以为学校提供更多的与国际上其他学校交流的机会。 blackbaord教学平台简单易用、本地化功能强，将多媒体的网络学习资源、网上学习社区以及网络技术结合于一体，形成一种全新的网络学习环境。汇集了大量的数据、档案资料、兴趣讨论组、新闻组等学习资源，形成了一个高度集成的资源库，轻松实现了信息资源的交流与共享。 在中国，blackbaord已成功地为北京师范大学，华南师范大学，中山大学，南京大学等学校用户构建了网络教学平台。

Blackboard网络学习平台在课堂教学中的设计

Blackboard 网络学习平台在课堂教学中的设计 Designing and Application of Web-based Course Platform Blackboard in Classroom Teaching: A Case Study in Second Language Acquisition//Su Baohua, Luo Xiaoying It is designed to develop the application of web-based course platform in the classroom teaching. The process of teaching and learning are united closely on the platform. In an effective way it shows the importance the bilingual teaching and increases the students ' active learning, which also expands the students ' learning domain s. Author 's address College of Chinese Language and Culture of Jinan University, Guangzhou, China 510610 1课程简介第二语言习得理论为暨南大学华文学院应用语言学系对外汉语专业以及华文教育系华文教育专业的本科专业必修课。这门课程开设的目的是帮助学生掌握一些基本的第二语言习得理论及研究方法。因此，结合Blackboard 网络学习平台（以下简称BB平台）为他们今后的对外汉语教学实践或进一步的研究工作做准备，具有非常重要的意义。 2实验教学单元 下面是第二语言习得理论课程的主要教学内容。

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间），并在职教新干线网站首页建立一个提供在线咨询服务的工作空间。要求各单位组织专门力量，按照申请注册机构空间——制定栏目方案——开展网页主体设计的顺序，仿照职教新干线模式进行建设，并明确一名负责人，负责本单位空间建设工作。 我校是首批重点国家级中等职业学校、省级示范性中职学校，早在2000年就着手校园网的建设，并于2010年进行全面升级改造，建成千兆主干、百兆桌面的数字化校园，配备了较为完善的校园信息管理系统。目前，以职教新干线为引领，通过应用带动，建设覆盖全校的网络学习交流互动平台已有基础。为加强我校职业教育信息化建设，实现优质职教资源共享、共用，我们将充分利用职教新干线，加速学校信息化进程，进一步提升我校信息化教学水平。为此特制定利用“职教新干线”提升学校信息化教学水平项目建设计划。 (一)、必要性 1、数字化校园是指挖掘先进的管理理念，以数字化信息和网络为基础，应用先进的信息化手段将信息技术融于教育的各个环节，通过全校所有部门的信息编码统一，使学校的所有信息能够实时自动的互连互通，资源得到充分的共享和利用，将学校内部相对独立分散的网络应用系统，进行了

Blackboard教学平台使用手册(学生版V1.0)

广东金融学院 Blackboard教学平台使用手册 （学生版V1.0） 校园网络中心编写 2010年10月

（一）平台基本操作 (3) （二）查看课程 (5) （三）提交作业及查看成绩 (7) （四）测验及查看成绩 (13) （五）论坛讨论 (18)

（一）平台基本操作 1．登陆及退出 BB平台 网址：https://www.wendangku.net/doc/c414341154.html, 用户名：学生学号 密码：初始密码与用户名相同（学生登陆平台后可以修改初始密码，修改方法见“2.修改密码”）为了保证帐户安全，请同学们在离开平台时，点页面上方的“注销”按钮安全退出平台后再关闭浏览器窗口，如图1。 图 1 2．修改密码 学生登陆平台后可以修改初始密码；若忘记密码，只能申请由系统管理员进行重设密码。 ?登陆 BB平台后，点击“我的首页”选项卡左边“工具”栏中的“个人信息”按钮，如图2。 图 2 ?在“个人信息”页面，点击“更改密码”，如图3。

图 3 ?输入新密码后点击“提交”，如图4，新密码要求为 5-8位数字、字母或下划线的组合。 图 4 注意：修改密码后，新密码请同学自行保管， BB系统不能查询，只能帮助同学重设密码。

（二）查看课程 1．登陆 BB平台后，点击“我的课程”选项卡，“课程列表”中列出学生选修的课程名称，点击某一门课程，如图6。 图 6 2．进入课程后，左边为课程菜单列表，右边默认显示“通知”内容，学生可及时查看教师发布的通知，如图7。 图 7 3．点击左边课程菜单中的“教学大纲”，即可在右边页面中查看教师上 传的教学大纲，如图8。

图 8 4．点击教师上传的教学大纲文件，在弹出的对话框中点击“打开”，如图9，将在当前页面显示教学大纲的内容，若点击“保存”可将教学大纲文件下载至本地计算机。 图 9 5．同理，点击课程菜单中的“教学进度”，可查看课程的教学进度表；点击课程菜单中的“课程文档”，可查看教师上传的课件；点击课程菜单中的“教师信息”，可查看任课教师的基本信息和答疑时间等。

数字化资源平台建设

数字化资源平台建设 随着计算机网络技术的发展，互联网的普及，教育也进入了网络的新时代，信息技术在教学中的应用也快速发展，信息化教学成为教育发展的新趋势。而数字化教学资源共享平台是实施信息化教学的基础，因此各学校开始重视数字化教学资源平台的建设，利用信息技术促进教学质量与效率的提高。下面结合本人的工作经历，分析如何进行数字化资源平台建设。 一、数字化教学资源共享平台构建体系 数字化教学资源共享平台是指在教育领域全面深入地运用现代信息技术来促进教育改革和教育发展，实现教育资源共建、共享，促使教学资源的统一管理，最终实现信息化教学的一个综合信息管理系统。它具有数字化、网络化、智能化和多媒体化的特点。现有大部分平台开发遵循教学性、科学性、开放性、应用性、层次性和经济性原则，基于SAN网络存储架构、TRS跨数据库检索技术和统一身份认证的门户网站的导航三层技术在校园局域网的基础上对数字化教学资源进行高度整合，从而实现校内资源的有效聚集与广泛共享、教学资源的个性化服务、确保查询速度、保护知识产权及资源的交互式应用。 而我校是一所中职学校，从资金到技术都没有这个实力，校园网的安全性较差，因此设了两台服务器，把校园网站等对外网的信息放到一个服务器上，把数字化资源平台和信息管理系统等放到另一个服务器上不对外网开放，这样不用怎么考虑外网的入浸。 二、注重技能培养需求开发优质资源 现代教育技术的发展对教育产生了全面、深刻的影响,不仅改革了教学模式和教学方法，还为我们呈现了一个教育现代化的宏伟蓝图。如何运用教育规律，利用现代教育技术手段，进行数字化资源建设已成为必然趋势。不同层次，不同类型的人才培养,需要适合其自身特点的教育信息化资源。以培养应用型人才为主，进行数字化资源建设也应注重对学生动手能力的培养，资源的构成可以以技术应用型媒体资源为主，同时注重理论与研究型媒体资源的开发。以计算机应用技术专业为例，在专业资源库建设前期，经过充分调研后，结合该专业人才培养方案，我们将应用案例的收集与开发及相关工具的使用作为该专业数字化资源建设的重点，同时做好相关技术素材的整理与制作工作。 内容与技术是数字化资源建设从不同角度划分的两个层面,内容表示该资源要呈现的信息内涵,技术指具体资源用何种媒体、什么样的方式来呈现。一般专业教师，对自身涉及到的专业比较了解，在数字化资源建设过程中制作一些PPT 课件还可以，但是要进行一些深层次数字化媒体资源的开发往往就无能为力了。学校在进行数字化资源整体规划中，要明确哪些是重点资源，对于这些资源可以按课程或专业列子项目成立开发小组，小组成员应由专业教师、IT方面或艺术方面的教师组成,专业教师负责具体资源的内容设计和脚本编写，然后由IT方面的教师选择合适的媒体形式并实现。 数字化教学资源的设计涉及到教育学理论、心理学理论、学习理论、教学设计、美学等多方面的知识,并非一个简单的过程。如何综合运用相关理论设计出

Blackboard网络教学平台介绍

Blackboard网络教学平台介绍 互联互动的网络学习环境 Blackboard致力于帮助院校打造一个真正的互联互动的网络学习环境（Networked Learning Environment，简称NLe），以实现互联网为教育带来的强大力量。在这个环境中，任何教师、学生和研究者都可以在任何方便的时间浏览内容、获取资源、评估教学效果、实现彼此的协作。 为实现NLe，Blackboard提供Blackboard教育软件（Blackboard Academic Suite?）以及与之配套的解决方案，为院校互联互动的网络学习环境提供专业技术支撑、赋予强大力量。 Blackboard教育软件是Blackboard公司基于NLe的理念精髓，体察全球各类院校的实际需求，并融入其在e-Learning行业多年的经验推出的全新力作。Blackboard教育软件提供了一套综合完整的解决方案，最大限度地优化和增强了此系列中每个独立产品的应用。该软件系列由以下3个平台组成：Blackboard教学管理平台、Blackboard门户社区平台、Blackboard资源管理平台 这3个平台涵盖院校教学信息化涉及的各个层面的需求：教学流程管理与监控、内容建设与共享、信息管理与发布、应用系统整合等。系列产品以“教学”、“联系”、“分享”为核心目标，为教育机构提供了丰富完善的工具和无限广阔的空间。

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Blackboard教学系统（Blackboard Learning System?） 产品功能简述 2005-5-8

授课、交流和测验 Blackboard Learning System?是行业领先的软件应用，用于加强虚拟学习环境、补充课堂教学和提供远程教学的平台。Blackboard Learning System?拥有一套强大的核心功能，使教师可以有效的管理课程、制作内容、生成作业和加强协作，从而协助学校达到与授课、交流和测验有关的重要目标。这些关键的功能包括： 课程管理： 用于管理课程网站或者其主要组成部分。课程管理功能有效的创建和设置课程（课程创建向导，课程模板），同时提供学期间的课程转移工具（课程复制，课程循环使用）和文档工具（课程导入/导出，课程存档，课程备份）。 课程内容制作： 直观的文本编辑器提供丰富的文本编辑界面，包括WYSIWYG（所见即所得）和拼写检查，用来创建有效的学习内容。快速编辑功能使教师可以在学生课程内容界面和教师课程界面间迅速切换。教师还可以导入由外部制作工具生成的电子学习内容，如Macromedia? Dreamweaver ? ,Microsoft? Frontpage?, 或任何和SCORM 配套的制作工具。 选择性内容发布： 教师可以根据课程内容和活动定制教学路径。内容项目、讨论、测验、作业或其他教学活动可以根据一系列的标准有选择的发布给学生。这些标准包括：日期/时间，用户名，用户组，机构角色，某一次考试或作业的成绩，或者该用户是否预习了下一内容单元。 课程大纲编辑器：

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中央财政重点支持专业的优质核心课程的教学资源在网上公开，实现优质资源共享。2009年建成学生自主学习环境，实现网上授课、网上辅导、网上答疑、网上批改作业功能，为“工学结合”教学模式在学院实施提供技术保证。 2、数字化图书馆建设 根据学院“十一五”发展规划，继续加强电子图书、文献资源库建设，全面升级图书馆现有硬件设备。新建一个80座电子阅览室；增加馆藏电子图书60万册；增加电子期刊30万册。通过建设，把图书馆建成全省同类院校一流水平的数字化图书馆。 3、公共资源服务平台建设 在现有9个多媒体教室基础上，新增2间48座语音教室，同时改造升级现有计算机教室2间，满足学院现代化教学要求，保证新增或改建后的教室能够达到国内同类院校先进标准。 4、多媒体应用平台建设 学院现有电子阅览室和办公用计算机很难满足一些包括图形图像制作处理、计算机软件等专业教师制作多媒体课件需求，拟购置10台高配计算机设备，以满足学院教学用多媒体课件制作要求。通过引进先进精品课录播系统，实现精品课程录制、编辑全过程自动化处理。 5、数据资源共享平台建设 学院现有教学资源库还不够完善，容量仅为400G，远远满足不了在校生网上自主学习需要，拟通过对现有FTP服务器进行硬件升级

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2010年第8期(下半月)软件导刊·教育技术 Blackboard 教学平台在《教学系统设计》 课程中的应用 王 辉 （西南大学西南民族教育与心理研究中心，重庆400715） 摘 要：鉴于Blackboard 网络教学平台在课程设计方面的优势，对《教学系统设计课程》通过该平台设计出高质 量的课程，能够促进学生对《教学系统设计》课程知识点的理解和掌握。阐述《教学系统设计》课程在Blackboard 网络教学平台的构建情况，以及构建教学系统设计课程网络教学平台的意义。 关键词：Blackboard ；教学平台；网络课程中图分类号：G434 文献标识码：A 文章编号：1672-7800（2010）08－0094－02 收稿日期:2010－06－17 作者简介:王辉（1985-），男，河南淮阳人，西南大学西南民族教育与心理研究中心硕士研究生，研究方向为新媒体与未来教育。 1Blackboard 网络教学平台简介 Blackboard 网络教学平台是由赛尔网络与美国毕博 （Blackboard ）公司共同开发的一种集声音、图像和文字于一体，专门用于加强虚拟学习环境、补充课堂教学并提供互动、交流的网络教学平台。它拥有一套强大的核心功能，是行业内领先的应用软件，可用于加强虚拟学习环境、补充课堂教学和提供远程教学的平台，使教师可以有效地管理课程、制作内容、生成作业和加强协作，从而协助学校达到与教学、交流和评价有关的重要目标。用户登录后可进入各自的控制面板界面，对自己所用的界面的功能模块进行配置。同时，教师和学生能够突破时间、地点的限制，通过控制面板对平台进行操作，教师也可以对平台内容进行组织管理。学生可以在线获取各种信息、学习资料，进行在线学习、考试等活动。目前我院投入使用的Black - board 平台主要包括5个主要的功能模块：①教学内容区模块。 它是教学平台的核心组成部分，主要供教师发布和管理教学资源以及作业的布置。包括课程信息、教学信息、课后作业、教学效果、课程特色、测试评价、政策支持和师生互动等内容。②课程工具模块。该模块为课程教学提供了多样化的工具，主要包括课程通知、课程日程表、职员信息、任务、发送电子邮件、讨论板、协作、数字收发箱、词汇表管理器、消息等。这些在线交流功能，可同时为用户提供讨论区的异步和虚拟教室的同步等交流工具，从而增强学习效果。③课程选项模块。主要用于管理课程网站或其主要组成部分，设置课程的显示界面、课程内容的重复使用以及课程资源的管理进行操作，主要包括管理课程菜单、课程设计、管理工具、循环使用课程、导入数据包、导出课程等。④用户管理模块。主要包括可对本课程的学生用户进 行注册或删除，并可设置学习小组以便进行小组讨论和其他类型的小组活动。包括列出/修改用户、注册用户、从课程中删除用户、管理小组等。⑤测试模块。主要由测试管理器、调查管理器、题库管理器、课程统计、成绩中心和成绩指示板组成，主要进行测试题库管理和成绩和数据统计管理。测验和调查主要用于教师开展在线的、自动评分的测验和调查。通过课程统计、成绩中心可以进行成绩和数据统计管理［1］。 2教学系统设计课程网络教学平台的构建 依据Blackboard 教学管理平台，对《教学系统设计》课程进 行系统设计，可以将该课程的教学资源不仅实施再生而且还可以进行延续使用也即是今年能使用，明年可以通过改进可以继续使用。该教学系统设计课程教授的对象是教育技术学专业的大三本科生。Blackboard 网络教学平台在教学中起到辅助学习的作用。在课程有限的情况下，教师可以通过Blackboard 平台进行课程设计，将每次课堂讲授的内容，教学电子材料（PPT 等课件）、课后作业、设计练习、期中考试、网上讨论等，对学习内容进行强化练习，最终能够根据学生的反馈和对学生的学习进行评价并对其进行综合分析，能够进一步对接下来的课程内容进行有针对性的设计。对于本课程，进行了教学内容设计、交互设计、课程管理设计以及评价设计。 对于Blackboard 网络平台为我们提供了14余种教学内容模块，本课程使用了其中的13种模块（图1）。 2.1教学内容设计 教学内容主要展示教师讲授的课程内容以及相关的辅助 教学材料。学生可以通过该Blackboard 网络教学平台在任何时候都能够进行自学、演练等。 资源建设 94

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数字化教学资源建设方 案 Company number：【WTUT-WT88Y-W8BBGB-BWYTT-19998】

安徽金寨职业学校 机电技术应用专业 数字化教学资源库建设方案 一、成立教学资源与信息化建设领导小组，将专业教学目标、专业教学标准、专业优质核心课程体系、实验实训指导、学习评价等整合处理，通过校园网络等实现课程资源网络化、信息化，建立具有四个功能、三大服务的共享型教学资源库。 二、推行“模块教学”、“情境教学”、“仿真教学”等教学模式改革。优化创新教学内容，提高信息化教学水平，广泛采用多媒体辅助教学手段，推动专业应用软件在教学中的应用，建设优质教材和特色学习资料，建设跨越围墙、跨越课堂、跨越时间的新型数字化立体教学资源库，按照一体化教学、一体化评价的要求，整合相关教学资源建立电子教案库、实训案例库、教学录像、相关图片、实物模型、试题库等组成机电技术应用专业的教学资源库，将多媒体技术最大可能的植入专业教学活动之中，利用教学软件、教学课件、多媒体教学平台、试题库、课程录像等多种媒体形式组成的机电专业教学资源库系统。 三、依托数字化校园建设，以创建精品资源为核心，组织建设多媒体教学课件，多媒体教学素材（含辅助教学软件、课程录像），教学案例，电子教案及电子教材，学生自主学习资料汇编（含考证题库）等，建立信息共享和自主学习平台上的立体化教学资源库，实现全校师生的网络教学资源的共享与应用。2016年初步建立并校内开放，2017年基本完成并对社会有限开放。为学生提供一个性能稳定、功能强大的自主学习平台；促进主动式、协作式、研究型、自主型学习，形成开放、高效的新型教学模式。立体化教学资源库组成如下图所示：

BB教学平台操作指南(学生用户版)

BB教学平台操作指南（学生版） 平台简介 Blackboard教学平台是国际领先的教学平台及服务提供商专门为教育机构开发研制的软件平台, 以“教学”、“联系”、“分享”为核心目标，提供一套综合、完整、优化的解决方案。Blackboard教学平台是以课程为中心集成网络“教”、“学”的网络教学环境。教师可以在平台上开设网络课程，学习者可以在教师的引导下，自主选择要学习的课程内容。不同学生之间，以及教师和学生之间可以根据“教和学”的需要进行讨论、交流。 开始使用 1、登录Blackboard教学平台 1）启动浏览器； 2）在地址栏处输入：https://www.wendangku.net/doc/c414341154.html,/，然后按下键盘上的回车键Enter。出现教学平台首页 3）学生用户登录教学平台的用户名为本人学号，初始密码与用户名相同 4) 在用户名输入框输入用户名如2010XXXXXXXX。 5) 在密码输入框中输入密码； 6) 单击登录按钮。

初步了解教学平台 ——认识我的主页 登录Blackboard 教学平台后页面上部会有一系列的选项卡,点击不同的选项，可见不同的内容，了解一个选项卡下的内容，对您能够尽快使用该教学平台将有很大帮助。 1．我的主页 登录Blackboard 教学平台后，首先看到的应是默认的选项卡“我的主页”，在此选项卡下用户可以看到自己可用的工具，自己学习的课程，系统及相关课程最新的通知，以及系统提供的日程表及快速指南等模块 2．认识选项卡 是平台内划分不同区域的标识。位于 Blackboard 教学平台的左上方。作为学生用户可以看到的选项卡有：我的主页，课程、院系工具 ● 我的主页：汇集了教师用户所教授和参与的课程信息以及可以使用的一些工具。 ● 课程：汇集了我校Blackboard 教学平台现有的所有在线课程。

高校数字化校园建设方案

高校数字化校园建设方案一、数字化校园建设目标通过数字化校园项目建设，构造能够满足数字化校园应用长期持续发展的应用框架，通过这一稳定、可扩展的应用框架为应用系统建设提供良好的支撑和服务。该应用框架将充分支持于学校的应用需求和未来发展，同时考虑到系统的总体拥有成本，必须采用先进的理念和思路，辅以成熟的、主流的、符合未来发展趋势的技术, 运用现代系统工程和项目管理规范标准，科学合理的进行建设。 建成完整统一、技术先进，覆盖全面、应用深入，咼效稳定、安全可靠的数字化校园，消除信息孤岛和应用孤岛，建立校级统一信息系统，实现部门间流程通畅，可平滑过渡到新一代技术，对校园的各项服务管理工作和广大教职工提供无所不在的一站式服务。提高工作效率，提高管理效率，提高决策效率，提高信息利用率, 提高核心竞争力，总体水平达到国内一流，满足教学、科研和管理工作的需要。具体目标就是实现“六个数字化”和“一站式服务”：1、环境数字化构建结构合理、使用方便、高速稳定、安全保密的基础网络。在此基础上，建立咼标准的数据共享中心和统身份认证及授权中心（Ucenter泛学校，统一门户平台以及集成应用软件平台，为实现更科学合理的高校数字化环境打下坚实的基础。 2、管理数字化构建覆盖全校工作流程的、协同的管理信息体系，通过管理信息的同步与共享，畅通学校的信息流，实现管理的科学化、自动化、精细化，突出以人为本的理念，提高管理效率，降低管理成本。 3、教学数字化构建综合教学管理的数字化环境，科学统一的配置教学资源，提高教师、教室、实训室等教学资源的利用率, 改革教学模式、手段与方法，丰富教学资源，提高教学效率与质量。 4、产学研数字化构建数字化产学研信息平台，为产学研工作者提供快捷、全面、权威的信息资源，实现教学、科研和实训一 体化，提供开放、协同、高效的数字化产学研环境，促进知识的产生、传播与管理。 5、学习数字化构建先进实用的网络教学平台，整合、丰富数字

数字化校园应用平台建设方案

数字化校园应用平台建设方案 承担部门：网络中心 领导小组组长：夏连学 成员：张瑞春宋全有马战宝党海宽 吴运友徐普民 数字化校园应用平台建设是以网络平台和共享型教学资源管理服务平台建设及其功能开发为基础，在网络技术、多媒体技术上建立起来的对教学资源、科研信息、综合管理、技术服务、生活服务等校园信息的收集、处理、整合、存储、制作、传输和应用，使数字资源得到充分优化利用的一种数字化虚拟教育环境。通过实现从环境（包括设备、教室等）、资源（如图书、讲义、课件等）到应用（包括教、学、管理、服务、办公等）的全部数字化，在传统校园基础上构建一个数字空间，以拓展现实校园的时间和空间维度，提升传统校园的运行效率，扩展传统校园的业务功能，最终实现教育过程的全面信息化，从而达到提高教学管理水平和效率的目的。 数字化校园应用平台建设包括：校园网络基础平台建设、共享型教学资源管理服务平台建设两个部分。 一、校园网络基础平台建设方案 （一）建设内容 校园网络基础平台分为“网络基础”、“网络中心机房系统”两个模块，建设内容及经费来源见表1。 表1 建设内容及经费来源 1、网络基础建设：在学院现有千兆以太网、主干网速率1000兆、桌面终

端100兆的基础上，提高校园网基础设施水平，构建万兆（10G）带宽的主干网络，做到技术先进、应用广泛、性能稳定；构建安全系统，形成一个包括认证、监测、追踪、加密、记录、路由管理、防火墙在内的安全管理系统，建设一个安全可靠的局域网。完成学生宿舍楼的光纤、双绞线等线路的布线以及交换机、学生宿舍分中心机房设备的安装和调试工作；艺术中心、图书馆、广场等公共场所采用有线网和无线网相结合，覆盖校园的每个角落。 逐步建立和完善校园网络安全体系，完善校园网络管理系统，升级校园网交换机，确保校园网中的所有交换机均能支持网络管理，支持802.1x身份认证。保证可以向第二代互联网平滑过渡。 2、网络中心机房系统：为提高校园网络的可靠性，对我院网络中心机房设备进行改造，主干采用交换机2台冗余，有条件的情况下，采用3台设备组成环状冗余网络。 依据学院建筑布局，对机房环境、供电系统、光纤连接、机柜及布线系统进行改造。使中心机房具有独立的UPS配电室，具备恒温、防静电、防雷功能。 拟购代表性仪器设备建设经费预算见表2。 表2 拟购代表性仪器设备建设经费预算 校园网络基础平台建设项目进度见表3

blackboard操作指南

第一部分：平台使用说明 (2) （一）平台简介 (2) （二）适用对象 (2) （三）教师需做的准备工作（必要操作） (2) （四）教师使用BB 平台流程图 (3) 第二部分：平台入门操作 (4) （一）平台入口与登陆平台（必要操作） (4) （二）认识平台 (4) （三）修改密码（可选操作） (5) （四）定制个人首页界面（可选操作） (6) （五）进入教授的课程（必要操作） (7) 第三部分：课程建设 (8) （一）课程结构设计（必要操作） (8) （二）添加课程内容（必要操作） (10) ●教学大纲（必要操作） (10) ●授课讲义（必要操作） (11) ●网络课件（可选操作） (11) ●精品课程网站（可选操作） (11) ●课外补充材料（可选操作） (11) ●随堂测验（可选操作） (11) ●课后作业（必要操作） (14) （三）课程存档和导入以及循环使用（有重复班的必要操作） (15) ●课程存档 (16) ●在新课程中导入课程文档 (16) ●课程循环 (17) 第四部分：互动教学 (18) （一）更新教师信息（必要操作） (18) （二）课程通知（必要操作） (19) （三）课程讨论板（可选操作） (20) （四）设定助教（可选操作） (23) （五）管理学习小组（可选操作） (24) 第五部分：学习跟踪与教学评价 (25) （一）学习跟踪；（必要操作） (25) （二）作业批改；（必要操作） (26) （三）试卷批改；（可选操作） (31) （四）教学评价；（可选操作） (32) 第六部分：常见问题及如何获得帮助 (34) （一）温馨提示 (34) （二）常见问题 (34) （三）如何获得帮助 (36)