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CHAPTER 11 THE UNIFICATION OF PHYSICS
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As was explained in the first chapter, it would be verydifficult to construct a complete unified1 theory of everything inthe universe all at one go. So instead we have made progressby finding partial theories that describe a limited range ofhappenings and by neglecting other effects or approximatingthem by certain numbers. (Chemistry, for example, allows us tocalculate the interactions of atoms, without knowing the internalstructure of an atom’s nucleus2.) Ultimately, however, one wouldhope to find a complete, consistent, unified theory that wouldinclude all these partial theories as approximations, and that didnot need to be adjusted to fit the facts by picking the valuesof certain arbitrary numbers in the theory. The quest for sucha theory is known as “the unification of physics.” Einstein spentmost of his later years unsuccessfully searching for a unifiedtheory, but the time was not ripe: there were partial theoriesfor gravity and the electromagnetic force, but very little wasknown about the nuclear forces. Moreover, Einstein refused tobelieve in the reality of quantum mechanics, despite theimportant role he had played in its development. Yet it seemsthat the uncertainty3 principle is a fundamental feature of theuniverse we live in. A successful unified theory must, therefore,necessarily incorporate this principle.
As I shall describe, the prospects4 for finding such a theoryseem to be much better now because we know so much moreabout the universe. But we must beware of overconfidence -we have had false dawns before! At the beginning of thiscentury, for example, it was thought that everything could beexplained in terms of the properties of continuous matter, suchas elasticity5 and heat conduction. The discovery of atomicstructure and the uncertainty principle put an emphatic6 end tothat. Then again, in 1928, physicist7 and Nobel Prize winnerMax Born told a group of visitors to Gottingen University,“Physics, as we know it, will be over in six months.” Hisconfidence was based on the recent discovery by Dirac of theequation that governed the electron. It was thought that asimilar equation would govern the proton, which was the onlyother particle known at the time, and that would be the end oftheoretical physics. However, the discovery of the neutron8 andof nuclear forces knocked that one on the head too. Havingsaid this, I still believe there are grounds for cautious optimismthat we may now be near the end of the search for theultimate laws of nature.
In previous chapters I have described general relativity, thepartial theory of gravity, and the partial theories that governthe weak, the strong, and the electromagnetic forces. The lastthree may be combined in so-called grand unified theories, orGUTs, which are not very satisfactory because they do notinclude gravity and because they contain a number ofquantities, like the relative masses of different particles, thatcannot be predicted from the theory but have to be chosen tofit observations. The main difficulty in finding a theory thatunifies gravity with the other forces is that general relativity is a“classical” theory; that is, it does not incorporate the uncertaintyprinciple of quantum mechanics. On the other hand, the otherpartial theories depend on quantum mechanics in an essentialway. A necessary first step, therefore, is to combine generalrelativity with the uncertainty principle. As we have seen, thiscan produce some remark-able consequences, such as blackholes not being black, and the universe not having anysingularities but being completely self-contained and without aboundary. The trouble is, as explained in Chapter 7, that theuncertainty principle means that even “empty” space is filledwith pairs of virtual particles and antiparticles. These pairswould have an infinite amount of energy and, therefore, byEinstein’s famous equation E = mc2, they would have aninfinite amount of mass. Their gravitational attraction would thuscurve up the universe to infinitely9 small size.
Rather similar, seemingly absurd infinities10 occur in the otherpartial theories, but in all these cases the infinities can becanceled out by a process called renormalization. This involvescanceling the infinities by introducing other infinities. Althoughthis technique is rather dubious11 mathematically, it does seem towork in practice, and has been used with these theories tomake predictions that agree with observations to anextraordinary degree of accuracy. Renormalization, however,does have a serious drawback from the point of view of tryingto find a complete theory, because it means that the actualvalues of the masses and the strengths of the forces cannot bepredicted from the theory, but have to be chosen to fit theobservations.
In attempting to incorporate the uncertainty principle intogeneral relativity, one has only two quantities that can beadjusted: the strength of gravity and the value of thecosmological constant. But adjusting these is not sufficient toremove all the infinities. One therefore has a theory that seemsto predict that certain quantities, such as the curvature ofspace-time, are really infinite, yet these quantities can beobserved and measured to be perfectly12 finite! This problem incombining general relativity and the uncertainty principle hadbeen suspected for some time, but was finally confirmed bydetailed calculations in 1972. Four years later, a possiblesolution, called “supergravity,” was suggested. The idea was tocombine the spin-2 particle called the graviton, which carriesthe gravitational force, with certain other particles of spin 3/2,1, ?, and 0. In a sense, all these particles could then beregarded as different aspects of the same “superparticle,” thusunifying the matter particles with spin ? and 3/2 with theforce-carrying particles of spin 0, 1, and 2. The virtualparticle/antiparticle pairs of spin ? and 3/2 would havenegative energy, and so would tend to cancel out the positiveenergy of the spin 2, 1, and 0 virtual pairs. This would causemany of the possible infinities to cancel out, but it wassuspected that some infinities might still remain. However, thecalculations required to find out whether or not there were anyinfinities left uncanceled were so long and difficult that no onewas prepared to undertake them. Even with a computer it wasreckoned it would take at least four years, and the chanceswere very high that one would make at least one mistake,probably more. So one would know one had the right answeronly if someone else repeated the calculation and got the sameanswer, and that did not seem very likely!
Despite these problems, and the fact that the particles in thesuper-gravity theories did not seem to match the observedparticles, most scientists believed that supergravity was probablythe right answer to the problem of the unification of physics. Itseemed the best way of unifying13 gravity with the other forces.
However, in 1984 there was a remarkable14 change of opinion infavor of what are called string theories. In these theories thebasic objects are not particles, which occupy a single point ofspace, but things that have a length but no other dimension,like an infinitely thin piece of string. These strings15 may haveends (the so-called open strings) or they may be joined upwith themselves in closed loops (closed strings) (Fig. 11.1 andFig. 11.2). A particle occupies one point of space at each instantof time. Thus its history can be represented by a line inspace-time (the “world-line”). A string, on the other hand,occupies a line in space at each moment of time. So its historyin space-time is a two-dimensional surface called theworld-sheet. (Any point on such a world-sheet can bedescribed by two numbers, one specifying16 the time and theother the position of the point on the string.) The world-sheetof an open string is a strip: its edges represent the pathsthrough space-time of the ends of the string (Fig. 11.1). Theworld-sheet of a closed string is a cylinder17 or tube (Fig. 11.2):
a slice through the tube is a circle, which represents theposition of the string at one particular time.
Two pieces of string can join together to form a singlestring; in the case of open strings they simply join at the ends(Fig. 11.3), while in the case of closed strings it is like the twolegs joining on a pair of trousers (Fig. 11.4). Similarly, a singlepiece of string can divide into two strings. In string theories,what were previously18 thought of as particles are now picturedas waves traveling down the string, like waves on a vibratingkite string. The emission19 or absorption of one particle byanother corresponds to the dividing or joining together ofstrings. For example, the gravitational force of the sun on theearth was pictured in particle theories as being caused by theemission of a graviton by a particle in the sun and itsabsorption by a particle in the earth (Fig. 11.5). In stringtheory, this process corresponds to an H-shaped tube or pipe(Fig. 11.6) (string theory is rather like plumbing20, in a way). Thetwo vertical21 sides of the H correspond to the particles in thesun and the earth, and the horizontal crossbar corresponds tothe graviton that travels between them.
String theory has a curious history. It was originally inventedin the late 1960s in an attempt to find a theory to describe thestrong force. The idea was that particles like the proton andthe neutron could be regarded as waves on a string. Thestrong forces between the particles would correspond to piecesof string that went between other bits of string, as in a spider’sweb. For this theory to give the observed value of the strongforce between particles, the strings had to be like rubber bandswith a pull of about ten tons.
In 1974 Joel Scherk from Paris and John Schwarz from theCalifornia Institute of Technology published a paper in whichthey showed that string theory could describe the gravitationalforce, but only if the tension in the string were very muchhigher, about a thousand million million million million millionmillion tons (1 with thirty-nine zeros after it). The predictions ofthe string theory would be just the same as those of generalrelativity on normal length scales, but they would differ at verysmall distances, less than a thousand million million millionmillion millionth of a centimeter (a centimeter divided by 1 withthirty-three zeros after it). Their work did not receive muchattention, however, because at just about that time most peopleabandoned the original string theory of the strong force infavor of the theory based on quarks and gluons, which seemedto fit much better with observations. Scherk died in tragiccircumstances (he suffered from diabetes22 and went into a comawhen no one was around to give him an injection of insulin).
So Schwarz was left alone as almost the only supporter ofstring theory, but now with the much higher pro-posed valueof the string tension.
In 1984 interest in strings suddenly revived, apparently23 fortwo reasons. One was that people were not really makingmuch progress toward showing that supergravity was finite orthat it could explain the kinds of particles that we observe. Theother was the publication of a paper by John Schwarz andMike Green of Queen Mary College, London, that showed thatstring theory might be able to explain the existence of particlesthat have a built-in left-handedness, like some of the particlesthat we observe. Whatever the reasons, a large number ofpeople soon began to work on string theory and a newversion was developed, the so-called heterotic string, whichseemed as if it might be able to explain the types of particlesthat we observe.
String theories also lead to infinities, but it is thought theywill all cancel out in versions like the heterotic string (thoughthis is not yet known for certain). String theories, however,have a bigger problem: they seem to be consistent only ifspace-time has either ten or twenty-six dimensions, instead ofthe usual four! Of course, extra space-time dimensions are acommonplace of science fiction indeed, they provide an idealway of overcoming the normal restriction24 of general relativitythat one cannot travel faster than light or back in time (seeChapter 10). The idea is to take a shortcut25 through the extradimensions. One can picture this in the following way. Imaginethat the space we live in has only two dimensions and iscurved like the surface of an anchor ring or torus (Fig. 11.7). Ifyou were on one side of the inside edge of the ring and youwanted to get to a point on the other side, you would have togo round the inner edge of the ring. However, if you wereable to travel in the third dimension, you could cut straightacross.
Why don’t we notice all these extra dimensions, if they arereally there? Why do we see only three space dimensions andone time dimension? The suggestion is that the otherdimensions are curved up into a space of very small size,something like a million million million million millionth of aninch. This is so small that we just don’t notice it: we see onlyone time dimension and three space dimensions, in whichspace-time is fairly flat. It is like the surface of a straw. If youlook at it closely, you see it is two-dimensional (the position ofa point on the straw is described by two numbers, the lengthalong the straw and the distance round the circular direction).
But if you look at it from a distance, you don’t see thethickness of the straw and it looks one-dimensional (theposition of a point is specified26 only by the length along thestraw). So it is with space-time: on a very small scale it isten-dimensional and highly curved, but on bigger scales youdon’t see the curvature or the extra dimensions. If this pictureis correct, it spells bad news for would-be space travelers: theextra dimensions would be far too small to allow a spaceshipthrough. However, it raises another major problem. Why shouldsome, but not all, of the dimensions be curled up into a smallball? Presumably, in the very early universe all the dimensionswould have been very curved. Why did one time dimensionand three space dimensions flatten27 out, while the otherdimensions remain tightly curled up?
One possible answer is the anthropic principle. Two spacedimensions do not seem to be enough to allow for thedevelopment of complicated beings like us. For example,two-dimensional animals living on a one-dimensional earth wouldhave to climb over each other in order to get past each other.
If a two-dimensional creature ate something it could not digestcompletely, it would have to bring up the remains28 the sameway it swallowed them, because if there were a passage rightthrough its body, it would divide the creature into two separatehalves: our two-dimensional being would fall apart (Fig. 11.8).
Similarly, it is difficult to see how there could be any circulationof the blood in a two-dimensional creature.
There would also be problems with more than three spacedimensions. The gravitational force between two bodies woulddecrease more rapidly with distance than it does in threedimensions. (In three dimensions, the gravitational force dropsto 1/4 if one doubles the distance. In four dimensions it woulddrop to 1/5, in five dimensions to 1/6, and so on.) Thesignificance of this is that the orbits of planets, like the earth,around the sun would be unstable29: the least disturbance30 froma circular orbit (such as would be caused by the gravitationalattraction of other planets) would result in the earth spiralingaway from or into the sun. We would either freeze or beburned up. In fact, the same behavior of gravity with distancein more than three space dimensions means that the sunwould not be able to exist in a stable state with pressurebalancing gravity. It would either fall apart or it would collapseto form a black hole. In either case, it would not be of muchuse as a source of heat and light for life on earth. On asmaller scale, the electrical forces that cause the electrons toorbit round the nucleus in an atom would behave in the sameway as gravitational forces. Thus the electrons would eitherescape from the atom altogether or would spiral into thenucleus. In either case, one could not have atoms as we knowthem.
It seems clear then that life, at least as we know it, canexist only in regions of space-time in which one time dimensionand three space dimensions are not curled up small. Thiswould mean that one could appeal to the weak anthropicprinciple, provided one could show that string theory does atleast allow there to be such regions of the universe - and itseems that indeed string theory does. There may well be otherregions of the universe, or other universes (whatever that maymean), in which all the dimensions are curled up small or inwhich more than four dimensions are nearly flat, but therewould be no intelligent beings in such regions to observe thedifferent number of effective dimensions.
Another problem is that there are at least four differentstring theories (open strings and three different closed stringtheories) and millions of ways in which the extra dimensionspredicted by string theory could be curled up. Why should justone string theory and one kind of curling up be picked out?
For a time there seemed no answer, and progress got boggeddown. Then, from about 1994, people started discovering whatare called dualities: different string theories and different waysof curling up the extra dimensions could lead to the sameresults in four dimensions. Moreover, as well as particles, whichoccupy a single point of space, and strings, which are lines,there were found to be other objects called p-branes, whichoccupied two-dimensional or higher-dimensional volumes inspace. (A particle can be regarded as a 0-brane and a stringas a 1-brane but there were also p-branes for p=2 to p=9.)What this seems to indicate is that there is a sort ofdemocracy among supergravity, string, and p-brane theories:
they seem to fit together but none can be said to be morefundamental than the others. They appear to be differentapproximations to some fundamental theory that are valid31 indifferent situations.
People have searched for this underlying32 theory, but withoutany success so far. However, I believe there may not be anysingle formulation of the fundamental theory any more than, asGodel showed, one could formulate33 arithmetic in terms of asingle set of axioms. Instead it may be like maps - you can’tuse a single map to describe the surface of the earth or ananchor ring: you need at least two maps in the case of theearth and four for the anchor ring to cover every point. Eachmap is valid only in a limited region, but different maps willhave a region of overlap34. The collection of maps provides acomplete description of the surface. Similarly, in physics it maybe necessary to use different formulations in different situations,but two different formulations would agree in situations wherethey can both be applied35. The whole collection of differentformulations could be regarded as a complete unified theory,though one that could not be expressed in terms of a singleset of postulates36.
But can there really be such a unified theory? Or are weperhaps just chasing a mirage37? There seem to be threepossibilities:
1. There really is a complete unified theory (or a collection ofoverlapping formulations), which we will someday discover if weare smart enough.
2. There is no ultimate theory of the universe, just aninfinite sequence of theories that describe the universe moreand more accurately38.
3. There is no theory of the universe: events cannot bepredicted beyond a certain extent but occur in a random39 andarbitrary manner.
Some would argue for the third possibility on the groundsthat if there were a complete set of laws, that would infringeGod’s freedom to change his mind and intervene in the world.
It’s a bit like the old paradox40: can God make a stone soheavy that he can’t lift it? But the idea that God might want tochange his mind is an example of the fallacy, pointed41 out bySt. Augustine, of imagining God as a being existing in time:
time is a property only of the universe that God created.
Presumably, he knew what he intended when he set it up!
With the advent42 of quantum mechanics, we have come torecognize that events cannot be predicted with completeaccuracy but that there is always a degree of uncertainty. Ifone likes, one could ascribe this randomness43 to the interventionof God, but it would be a very strange kind of intervention44:
there is no evidence that it is directed toward any purpose.
Indeed, if it were, it would by definition not be random. Inmodern times, we have effectively removed the third possibilityabove by redefining the goal of science: our aim is to formulatea set of laws that enables us to predict events only up to thelimit set by the uncertainty principle.
The second possibility, that there is an infinite sequence ofmore and more refined theories, is in agreement with all ourexperience so far. On many occasions we have increased thesensitivity of our measurements or made a new class ofobservations, only to discover new phenomena45 that were notpredicted by the existing theory, and to account for these wehave had to develop a more advanced theory. It wouldtherefore not be very surprising if the present generation ofgrand unified theories was wrong in claiming that nothingessentially new will happen between the electroweak unificationenergy of about 100 GeV and the grand unification energy ofabout a thousand million million GeV. We might indeed expectto find several new layers of structure more basic than thequarks and electrons that we now regard as “elementary”
particles.
However, it seems that gravity may provide a limit to thissequence of “boxes within boxes.” If one had a particle with anenergy above what is called the Planck energy, ten millionmillion million GeV (1 followed by nineteen zeros), its masswould be so concentrated that it would cut itself off from therest of the universe and form a little black hole. Thus it doesseem that the sequence of more and more refined theoriesshould have some limit as we go to higher and higherenergies, so that there should be some ultimate theory of theuniverse. Of course, the Planck energy is a very long way fromthe energies of around a hundred GeV, which are the mostthat we can produce in the laboratory at the present time. Weshall not bridge that gap with particle accelerators in theforeseeable future! The very early stages of the universe,however, are an arena46 where such energies must haveoccurred. I think that there is a good chance that the study ofthe early universe and the requirements of mathematicalconsistency will lead us to a complete unified theory within thelifetime of some of us who are around today, always presumingwe don’t blow ourselves up first.
What would it mean if we actually did discover the ultimatetheory of the universe? As was explained in Chapter 1, wecould never be quite sure that we had indeed found thecorrect theory, since theories can’t be proved. But if the theorywas mathematically consistent and always gave predictions thatagreed with observations, we could be reasonably confident thatit was the right one. It would bring to an end a long andglorious chapter in the history of humanity’s intellectual struggleto understand the universe. But it would also revolutionize theordinary person’s understanding of the laws that govern theuniverse. In Newton’s time it was possible for an educatedperson to have a grasp of the whole of human knowledge, atleast in outline. But since then, the pace of the development ofscience has made this impossible. Because theories are alwaysbeing changed to account for new observations, they are neverproperly digested or simplified so that ordinary people canunderstand them. You have to be a specialist, and even thenyou can only hope to have a proper grasp of a smallproportion of the scientific theories. Further, the rate ofprogress is so rapid that what one learns at school oruniversity is always a bit out of date. Only a few people cankeep up with the rapidly advancing frontier of knowledge, andthey have to devote their whole time to it and specialize in asmall area. The rest of the population has little idea of theadvances that are being made or the excitement they aregenerating. Seventy years ago, if Eddington is to be believed,only two people understood the general theory of relativity.
Nowadays tens of thousands of university graduates do, andmany millions of people are at least familiar with the idea. If acomplete unified theory was discovered, it would only be amatter of time before it was digested and simplified in thesame way and taught in schools, at least in outline. We wouldthen all be able to have some understanding of the laws thatgovern the universe and are responsible for our existence.
Even if we do discover a complete unified theory, it wouldnot mean that we would be able to predict events in general,for two reasons. The first is the limitation that the uncertaintyprinciple of quantum mechanics sets on our powers ofprediction. There is nothing we can do to get around that. Inpractice, however, this first limitation is less restrictive than thesecond one. It arises from the fact that we could not solve theequations of the theory exactly, except in very simple situations.
(We cannot even solve exactly for the motion of three bodiesin Newton’s theory of gravity, and the difficulty increases withthe number of bodies and the complexity47 of the theory.) Wealready know the laws that govern the behavior of matterunder all but the most extreme conditions. In particular, weknow the basic laws that underlie48 all of chemistry and biology.
Yet we have certainly not reduced these subjects to the statusof solved problems: we have, as yet, had little success inpredicting human behavior from mathematical equations! Soeven if we do find a complete set of basic laws, there will stillbe in the years ahead the intellectually challenging task ofdeveloping better approximation methods, so that we can makeuseful predictions of the probable outcomes in complicated andrealistic situations. A complete, consistent, unified theory is onlythe first step: our goal is a complete understanding of theevents around us, and of our own existence.


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1 unified 40b03ccf3c2da88cc503272d1de3441c     
(unify 的过去式和过去分词); 统一的; 统一标准的; 一元化的
参考例句:
  • The teacher unified the answer of her pupil with hers. 老师核对了学生的答案。
  • The First Emperor of Qin unified China in 221 B.C. 秦始皇于公元前221年统一中国。
2 nucleus avSyg     
n.核,核心,原子核
参考例句:
  • These young people formed the nucleus of the club.这些年轻人成了俱乐部的核心。
  • These councils would form the nucleus of a future regime.这些委员会将成为一个未来政权的核心。
3 uncertainty NlFwK     
n.易变,靠不住,不确知,不确定的事物
参考例句:
  • Her comments will add to the uncertainty of the situation.她的批评将会使局势更加不稳定。
  • After six weeks of uncertainty,the strain was beginning to take its toll.6个星期的忐忑不安后,压力开始产生影响了。
4 prospects fkVzpY     
n.希望,前途(恒为复数)
参考例句:
  • There is a mood of pessimism in the company about future job prospects. 公司中有一种对工作前景悲观的情绪。
  • They are less sanguine about the company's long-term prospects. 他们对公司的远景不那么乐观。
5 elasticity 8jlzp     
n.弹性,伸缩力
参考例句:
  • The skin eventually loses its elasticity.皮肤最终会失去弹性。
  • Every sort of spring has a definite elasticity.每一种弹簧都有一定的弹性。
6 emphatic 0P1zA     
adj.强调的,着重的;无可置疑的,明显的
参考例句:
  • Their reply was too emphatic for anyone to doubt them.他们的回答很坚决,不容有任何人怀疑。
  • He was emphatic about the importance of being punctual.他强调严守时间的重要性。
7 physicist oNqx4     
n.物理学家,研究物理学的人
参考例句:
  • He is a physicist of the first rank.他是一流的物理学家。
  • The successful physicist never puts on airs.这位卓有成就的物理学家从不摆架子。
8 neutron neutron     
n.中子
参考例句:
  • Neutron is neutral and slightly heavier than the proton.中子是中性的,比质子略重。
  • Based on the neutron energy,the value of weighting factor was given.根据中子能量给出了相应的辐射权重因子的数值。
9 infinitely 0qhz2I     
adv.无限地,无穷地
参考例句:
  • There is an infinitely bright future ahead of us.我们有无限光明的前途。
  • The universe is infinitely large.宇宙是无限大的。
10 infinities c7c429f6d6793c16bc467ea427df1c7f     
n.无穷大( infinity的名词复数 );无限远的点;无法计算的量;无限大的量
参考例句:
11 dubious Akqz1     
adj.怀疑的,无把握的;有问题的,靠不住的
参考例句:
  • What he said yesterday was dubious.他昨天说的话很含糊。
  • He uses some dubious shifts to get money.他用一些可疑的手段去赚钱。
12 perfectly 8Mzxb     
adv.完美地,无可非议地,彻底地
参考例句:
  • The witnesses were each perfectly certain of what they said.证人们个个对自己所说的话十分肯定。
  • Everything that we're doing is all perfectly above board.我们做的每件事情都是光明正大的。
13 unifying 18f99ec3e0286dcc4f6f318a4d8aa539     
使联合( unify的现在分词 ); 使相同; 使一致; 统一
参考例句:
  • In addition, there were certain religious bonds of a unifying kind. 此外,他们还有某种具有一种统一性质的宗教上的结合。
  • There is a unifying theme, and that is the theme of information flow within biological systems. 我们可以用一个总的命题,把生物学系统内的信息流来作为这一研究主题。
14 remarkable 8Vbx6     
adj.显著的,异常的,非凡的,值得注意的
参考例句:
  • She has made remarkable headway in her writing skills.她在写作技巧方面有了长足进步。
  • These cars are remarkable for the quietness of their engines.这些汽车因发动机没有噪音而不同凡响。
15 strings nh0zBe     
n.弦
参考例句:
  • He sat on the bed,idly plucking the strings of his guitar.他坐在床上,随意地拨着吉他的弦。
  • She swept her fingers over the strings of the harp.她用手指划过竖琴的琴弦。
16 specifying ca4cf95d0de82d4463dfea22d3f8c836     
v.指定( specify的现在分词 );详述;提出…的条件;使具有特性
参考例句:
  • When we describe what the action will affect, we are specifying the noun of the sentence. 当描述动作会影响到什么时,我们指定组成句子的名词。 来自About Face 3交互设计精髓
  • Procurement section only lists opportunistic infection drugs without specifying which drugs. 采购部分只说明有治疗机会性感染的药物,但并没有说明是什么药物。 来自互联网
17 cylinder rngza     
n.圆筒,柱(面),汽缸
参考例句:
  • What's the volume of this cylinder?这个圆筒的体积有多少?
  • The cylinder is getting too much gas and not enough air.汽缸里汽油太多而空气不足。
18 previously bkzzzC     
adv.以前,先前(地)
参考例句:
  • The bicycle tyre blew out at a previously damaged point.自行车胎在以前损坏过的地方又爆开了。
  • Let me digress for a moment and explain what had happened previously.让我岔开一会儿,解释原先发生了什么。
19 emission vjnz4     
n.发出物,散发物;发出,散发
参考例句:
  • Rigorous measures will be taken to reduce the total pollutant emission.采取严格有力措施,降低污染物排放总量。
  • Finally,the way to effectively control particulate emission is pointed out.最后,指出有效降低颗粒排放的方向。
20 plumbing klaz0A     
n.水管装置;水暖工的工作;管道工程v.用铅锤测量(plumb的现在分词);探究
参考例句:
  • She spent her life plumbing the mysteries of the human psyche. 她毕生探索人类心灵的奥秘。
  • They're going to have to put in new plumbing. 他们将需要安装新的水管。 来自《简明英汉词典》
21 vertical ZiywU     
adj.垂直的,顶点的,纵向的;n.垂直物,垂直的位置
参考例句:
  • The northern side of the mountain is almost vertical.这座山的北坡几乎是垂直的。
  • Vertical air motions are not measured by this system.垂直气流的运动不用这种系统来测量。
22 diabetes uPnzu     
n.糖尿病
参考例句:
  • In case of diabetes, physicians advise against the use of sugar.对于糖尿病患者,医生告诫他们不要吃糖。
  • Diabetes is caused by a fault in the insulin production of the body.糖尿病是由体內胰岛素分泌失调引起的。
23 apparently tMmyQ     
adv.显然地;表面上,似乎
参考例句:
  • An apparently blind alley leads suddenly into an open space.山穷水尽,豁然开朗。
  • He was apparently much surprised at the news.他对那个消息显然感到十分惊异。
24 restriction jW8x0     
n.限制,约束
参考例句:
  • The park is open to the public without restriction.这个公园对公众开放,没有任何限制。
  • The 30 mph speed restriction applies in all built-up areas.每小时限速30英里适用于所有建筑物聚集区。
25 shortcut Cyswg     
n.近路,捷径
参考例句:
  • He was always looking for a shortcut to fame and fortune.他总是在找成名发财的捷径。
  • If you take the shortcut,it will be two li closer.走抄道去要近2里路。
26 specified ZhezwZ     
adj.特定的
参考例句:
  • The architect specified oak for the wood trim. 那位建筑师指定用橡木做木饰条。
  • It is generated by some specified means. 这是由某些未加说明的方法产生的。
27 flatten N7UyR     
v.把...弄平,使倒伏;使(漆等)失去光泽
参考例句:
  • We can flatten out a piece of metal by hammering it.我们可以用锤子把一块金属敲平。
  • The wrinkled silk will flatten out if you iron it.发皱的丝绸可以用熨斗烫平。
28 remains 1kMzTy     
n.剩余物,残留物;遗体,遗迹
参考例句:
  • He ate the remains of food hungrily.他狼吞虎咽地吃剩余的食物。
  • The remains of the meal were fed to the dog.残羹剩饭喂狗了。
29 unstable Ijgwa     
adj.不稳定的,易变的
参考例句:
  • This bookcase is too unstable to hold so many books.这书橱很不结实,装不了这么多书。
  • The patient's condition was unstable.那患者的病情不稳定。
30 disturbance BsNxk     
n.动乱,骚动;打扰,干扰;(身心)失调
参考例句:
  • He is suffering an emotional disturbance.他的情绪受到了困扰。
  • You can work in here without any disturbance.在这儿你可不受任何干扰地工作。
31 valid eiCwm     
adj.有确实根据的;有效的;正当的,合法的
参考例句:
  • His claim to own the house is valid.他主张对此屋的所有权有效。
  • Do you have valid reasons for your absence?你的缺席有正当理由吗?
32 underlying 5fyz8c     
adj.在下面的,含蓄的,潜在的
参考例句:
  • The underlying theme of the novel is very serious.小说隐含的主题是十分严肃的。
  • This word has its underlying meaning.这个单词有它潜在的含义。
33 formulate L66yt     
v.用公式表示;规划;设计;系统地阐述
参考例句:
  • He took care to formulate his reply very clearly.他字斟句酌,清楚地做了回答。
  • I was impressed by the way he could formulate his ideas.他陈述观点的方式让我印象深刻。
34 overlap tKixw     
v.重叠,与…交叠;n.重叠
参考例句:
  • The overlap between the jacket and the trousers is not good.夹克和裤子重叠的部分不好看。
  • Tiles overlap each other.屋瓦相互叠盖。
35 applied Tz2zXA     
adj.应用的;v.应用,适用
参考例句:
  • She plans to take a course in applied linguistics.她打算学习应用语言学课程。
  • This cream is best applied to the face at night.这种乳霜最好晚上擦脸用。
36 postulates a2e60978b0d3ff36cce5760c726afc83     
v.假定,假设( postulate的第三人称单数 )
参考例句:
  • They proclaimed to be eternal postulates of reason and justice. 他们宣称这些原则是理性和正义的永恒的要求。 来自辞典例句
  • The school building programme postulates an increase in educational investment. 修建校舍的计画是在增加教育经费的前提下拟定的。 来自辞典例句
37 mirage LRqzB     
n.海市蜃楼,幻景
参考例句:
  • Perhaps we are all just chasing a mirage.也许我们都只是在追逐一个幻想。
  • Western liberalism was always a mirage.西方自由主义永远是一座海市蜃楼。
38 accurately oJHyf     
adv.准确地,精确地
参考例句:
  • It is hard to hit the ball accurately.准确地击中球很难。
  • Now scientists can forecast the weather accurately.现在科学家们能准确地预报天气。
39 random HT9xd     
adj.随机的;任意的;n.偶然的(或随便的)行动
参考例句:
  • The list is arranged in a random order.名单排列不分先后。
  • On random inspection the meat was found to be bad.经抽查,发现肉变质了。
40 paradox pAxys     
n.似乎矛盾却正确的说法;自相矛盾的人(物)
参考例句:
  • The story contains many levels of paradox.这个故事存在多重悖论。
  • The paradox is that Japan does need serious education reform.矛盾的地方是日本确实需要教育改革。
41 pointed Il8zB4     
adj.尖的,直截了当的
参考例句:
  • He gave me a very sharp pointed pencil.他给我一支削得非常尖的铅笔。
  • She wished to show Mrs.John Dashwood by this pointed invitation to her brother.她想通过对达茨伍德夫人提出直截了当的邀请向她的哥哥表示出来。
42 advent iKKyo     
n.(重要事件等的)到来,来临
参考例句:
  • Swallows come by groups at the advent of spring. 春天来临时燕子成群飞来。
  • The advent of the Euro will redefine Europe.欧元的出现将重新定义欧洲。
43 randomness af1c2e393e31ba3c5a65a5ccc64d0789     
n.随意,无安排;随机性
参考例句:
  • The randomness is attributed to the porous medium. 随机性起因于多孔介质。 来自辞典例句
  • Einstein declared that randomness rather than lawfulness is the characteristic of natural events. 爱因斯坦宣称自然现象的特征为不可测性而不是规律化。 来自辞典例句
44 intervention e5sxZ     
n.介入,干涉,干预
参考例句:
  • The government's intervention in this dispute will not help.政府对这场争论的干预不会起作用。
  • Many people felt he would be hostile to the idea of foreign intervention.许多人觉得他会反对外来干预。
45 phenomena 8N9xp     
n.现象
参考例句:
  • Ade couldn't relate the phenomena with any theory he knew.艾德无法用他所知道的任何理论来解释这种现象。
  • The object of these experiments was to find the connection,if any,between the two phenomena.这些实验的目的就是探索这两种现象之间的联系,如果存在着任何联系的话。
46 arena Yv4zd     
n.竞技场,运动场所;竞争场所,舞台
参考例句:
  • She entered the political arena at the age of 25. 她25岁进入政界。
  • He had not an adequate arena for the exercise of his talents.他没有充分发挥其才能的场所。
47 complexity KO9z3     
n.复杂(性),复杂的事物
参考例句:
  • Only now did he understand the full complexity of the problem.直到现在他才明白这一问题的全部复杂性。
  • The complexity of the road map puzzled me.错综复杂的公路图把我搞糊涂了。
48 underlie AkSwu     
v.位于...之下,成为...的基础
参考例句:
  • Technology improvements underlie these trends.科技进步将成为此发展趋势的基础。
  • Many facts underlie my decision.我的决定是以许多事实为依据的。


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