Chapter One
Part I
The Edge of Knowledge
Tied Up with String
Calling it a cover-up would be far too dramatic. But for more than halfa century--even in the midst of some of the greatest scientificachievements in history--physicists have been quietly aware of a darkcloud looming on a distant horizon. The problem is this: There are twofoundational pillars upon which modern physics rests. One is Albert Einstein'sgeneral relativity, which provides a theoretical framework for understandingthe universe on the largest of scales: stars, galaxies, clustersof galaxies, and beyond to the immense expanse of the universe itself.The other is quantum mechanics, which provides a theoretical frameworkfor understanding the universe on the smallest of scales: molecules, atoms,and all the way down to subatomic particles like electrons and quarks.Through years of research, physicists have experimentally confirmed to almostunimaginable accuracy virtually all predictions made by each ofthese theories. But these same theoretical tools inexorably lead to anotherdisturbing conclusion: As they are currently formulated, general relativityand quantum mechanics cannot both be right. The two theories underlyingthe tremendous progress of physics during the last hundred years--progressthat has explained the expansion of the heavens and thefundamental structure of matter--are mutually incompatible.
If you have not heard previously about this ferocious antagonism youmay be wondering why. The answer is not hard to come by. In all but themost extreme situations, physicists study things that are either small andlight (like atoms and their constituents) or things that are huge and heavy(like stars and galaxies), but not both. This means that they need use onlyquantum mechanics or only general relativity and can, with a furtiveglance, shrug off the barking admonition of the other. For fifty years thisapproach has not been quite as blissful as ignorance, but it has been prettyclose.
But the universe can be extreme. In the central depths of a blackhole an enormous mass is crushed to a minuscule size. At the moment of thebig bang the whole of the universe erupted from a microscopic nuggetwhose size makes a grain of sand look colossal. These are realms that aretiny and yet incredibly massive, therefore requiring that both quantum mechanicsand general relativity simultaneously be brought to bear. For reasonsthat will become increasingly clear as we proceed, the equations ofgeneral relativity and quantum mechanics, when combined, begin toshake, rattle, and gush with steam like a red-lined automobile. Put lessfiguratively, well-posed physical questions elicit nonsensical answers fromthe unhappy amalgam of these two theories. Even if you are willing to keepthe deep interior of a black hole and the beginning of the universeshrouded in mystery, you can't help feeling that the hostility betweenquantum mechanics and general relativity cries out for a deeper level ofunderstanding. Can it really be that the universe at its most fundamentallevel is divided, requiring one set of laws when things are large and adifferent, incompatible set when things are small?
Superstring theory, a young upstart compared with the venerable edificesof quantum mechanics and general relativity, answers with a resoundingno. Intense research over the past decade by physicists andmathematicians around the world has revealed that this new approach todescribing matter at its most fundamental level resolves the tension betweengeneral relativity and quantum mechanics. In fact, superstring theoryshows more: Within this new framework, general relativity andquantum mechanics require one another for the theory to make sense.According to superstring theory, the marriage of the laws of the large and thesmall is not only happy but inevitable.
That's part of the good news. But superstring theory--string theory, forshort--takes this union one giant step further. For three decades, Einsteinsought a unified theory of physics, one that would interweave all of nature'sforces and material constituents within a single theoretical tapestry.He failed. Now, at the dawn of the new millennium, proponents of stringtheory claim that the threads of this elusive unified tapestry finally havebeen revealed. String theory has the potential to show that all of the wondroushappenings in the universe--from the frantic dance of subatomicquarks to the stately waltz of orbiting binary stars, from the primordialfireball of the big bang to the majestic swirl of heavenly galaxies--arereflections of one grand physical principle, one master equation.
Because these features of string theory require that we drasticallychange our understanding of space, time, and matter, they will take sometime to get used to, to sink in at a comfortable level. But as shall becomeclear, when seen in its proper context, string theory emerges as a dramaticyet natural outgrowth of the revolutionary discoveries of physics during thepast hundred years. In fact, we shall see that the conflict between generalrelativity and quantum mechanics is actually not the first, but the third ina sequence of pivotal conflicts encountered during the past century, eachof whose resolution has resulted in a stunning revision of our understandingof the universe.
The Three Conflicts
The first conflict, recognized as far back as the late 1800s, concerns puzzlingproperties of the motion of light. Briefly put, according to Isaac Newton'slaws of motion, if you run fast enough you can catch up with adeparting beam of light, whereas according to James Clerk Maxwell's lawsof electromagnetism, you can't. As we will discuss in Chapter 2, Einsteinresolved this conflict through his theory of special relativity, and in sodoing completely overturned our understanding of space and time. Accordingto special relativity, no longer can space and time be thought of asuniversal concepts set in stone, experienced identically by everyone.Rather, space and time emerged from Einstein's reworking as malleableconstructs whose form and appearance depend on one's state of motion.
The development of special relativity immediately set the stage for thesecond conflict. One conclusion of Einstein's work is that no object--infact, no influence or disturbance of any sort--can travel faster than thespeed of light. But, as we shall discuss in Chapter 3, Newton's experimentallysuccessful and intuitively pleasing universal theory of gravitationinvolves influences that are transmitted over vast distances of spaceinstantaneously. It was Einstein, again, who stepped in and resolved theconflict by offering a new conception of gravity with his 1915 general theoryof relativity. Just as special relativity overturned previous conceptionsof space and time, so too did general relativity. Not only are space and timeinfluenced by one's state of motion, but they can warp and curve in responseto the presence of matter or energy. Such distortions to the fabricof space and time, as we shall see, transmit the force of gravity from oneplace to another. Space and time, therefore, can no longer to be thoughtof as an inert backdrop on which the events of the universe play themselvesout; rather, through special and then general relativity, they are intimateplayers in the events themselves.
Once again the pattern repeated itself: The discovery of general relativity,while resolving one conflict, led to another. Over the course of thethree decades beginning in 1900, physicists developed quantum mechanics(discussed in Chapter 4) in response to a number of glaring problemsthat arose when nineteenth-century conceptions of physics wereapplied to the microscopic world. And as mentioned above, the third anddeepest conflict arises from the incompatibility between quantum mechanicsand general relativity. As we will see in Chapter 5, the gently curvinggeometrical form of space emerging from general relativity is atloggerheads with the frantic, roiling, microscopic behavior of the universeimplied by quantum mechanics. As it was not until the mid-1980s thatstring theory offered a resolution, this conflict is rightly called the centralproblem of modern physics. Moreover, building on special and general relativity,string theory requires its own severe revamping of our conceptionsof space and time. For example, most of us take for granted that our universehas three spatial dimensions. But this is not so according to stringtheory, which claims that our universe has many more dimensions thanmeet the eye--dimensions that are tightly curled into the folded fabricof the cosmos. So central are these remarkable insights into the natureof space and time that we shall use them as a guiding theme in all thatfollows. String theory, in a real sense, is the story of space and time sinceEinstein.
To appreciate what string theory actually is, we need to take a step backand briefly describe what we have learned during the last century aboutthe microscopic structure of the universe.
The Universe at Its Smallest: What We Know about Matter
The ancient Greeks surmised that the stuff of the universe was made upof tiny "uncuttable" ingredients that they called atoms. Just as theenormous number of words in an alphabetic language is built up from thewealth of combinations of a small number of letters, they guessed that thevast range of material objects might also result from combinations of asmall number of distinct, elementary building blocks. It was a prescientguess. More than 2,000 years later we still believe it to be true, althoughthe identity of the most fundamental units has gone through numerous revisions.In the nineteenth century scientists showed that many familiarsubstances such as oxygen and carbon had a smallest recognizable constituent;following in the tradition laid down by the Greeks, they calledthem atoms. The name stuck, but history has shown it to be a misnomer,since atoms surely are "cuttable." By the early 1930s the collective worksof J. J. Thomson, Ernest Rutherford, Niels Bohr, and James Chadwick hadestablished the solar system-like atomic model with which most of us arefamiliar. Far from being the most elementary material constituent, atomsconsist of a nucleus, containing protons and neutrons, that is surroundedby a swarm of orbiting electrons.
For a while many physicists thought that protons, neutrons, and electronswere the Greeks' "atoms." But in 1968 experimenters at the StanfordLinear Accelerator Center, making use of the increased capacity of technologyto probe the microscopic depths of matter, found that protons andneutrons are not fundamental, either. Instead they showed that each consistsof three smaller particles, called quarks--a whimsical name takenfrom a passage in James Joyce's Finnegan's Wake by the theoreticalphysicist Murray Gell-Mann, who previously had surmised their existence. Theexperimenters confirmed that quarks themselves come in two varieties,which were named, a bit less creatively, up and down. A protonconsists of two up-quarks and a down-quark; a neutron consists of twodown-quarks and an up-quark.
Everything you see in the terrestrial world and the heavens above appearsto be made from combinations of electrons, up-quarks, and down-quarks.No experimental evidence indicates that any of these threeparticles is built up from something smaller. But a great deal of evidenceindicates that the universe itself has additional particulate ingredients. Inthe mid-1950s, Frederick Reines and Clyde Cowan found conclusive experimentalevidence for a fourth kind of fundamental particle called aneutrino--a particle whose existence was predicted in the early 1930s byWolfgang Pauli. Neutrinos proved very difficult to find because they areghostly particles that only rarely interact with other matter: an average-energyneutrino can easily pass right through many trillion miles of leadwithout the slightest effect on its motion. This should give you significantrelief, because right now as you read this, billions of neutrinos ejected intospace by the sun are passing through your body and the earth as well, aspart of their lonely journey through the cosmos. In the late 1930s, anotherparticle called a muon--identical to an electron except that a muon isabout 200 times heavier--was discovered by physicists studying cosmicrays (showers of particles that bombard earth from outer space). Becausethere was nothing in the cosmic order, no unsolved puzzle, no tailor-madeniche, that necessitated the muon's existence, the Nobel Prize-winningparticle physicist Isidor Isaac Rabi greeted the discovery of the muon witha less than enthusiastic "Who ordered that?" Nevertheless, there it was.And more was to follow.
Using ever more powerful technology, physicists have continued toslam bits of matter together with ever increasing energy, momentarilyrecreating conditions unseen since the big bang. In the debris they havesearched for new fundamental ingredients to add to the growing list ofparticles. Here is what they have found: four more quarks-charm, strange,bottom, and top--and another even heavier cousin of the electron,called a tau, as well as two other particles with properties similar tothe neutrino (called the muon-neutrino and tau-neutrino to distinguishthem from the original neutrino, now called the electron-neutrino).These particles are produced through high-energy collisions and exist onlyephemerally; they are not constituents of anything we typically encounter. Buteven this is not quite the end of the story. Each of these particles has anantiparticle partner--a particle of identical mass but opposite incertain other respects such as its electric charge (as well as its charges withrespect to other forces discussed below). For instance, the antiparticle of anelectron is called a positron--it has exactly the same mass as anelectron, but its electric charge is +1 whereas the electric charge of theelectron is -1. When in contact, matter and antimatter can annihilate oneanother to produce pure energy--that's why there is extremely little naturallyoccurring antimatter in the world around us.
Physicists have recognized a pattern among these particles, displayedin Table 1.1. The matter particles neatly fall into three groups, which areoften called families. Each family contains two of the quarks, anelectron or one of its cousins, and one of the neutrino species. Thecorresponding particle types across the three families have identical propertiesexcept for their mass, which grows larger in each successive family. The upshotis that physicists have now probed the structure of matter to scales of abouta billionth of a billionth of a meter and shown that everythingencountered to date--whether it occurs naturally or is produced artificiallywith giant atom-smashers--consists of some combination of particles from thesethree families and their antimatter partners.
A glance at Table 1.1 will no doubt leave you with an even strongersense of Rabi's bewilderment at the discovery of the muon. The arrangementinto families at least gives some semblance of order, but innumerable"whys" leap to the fore. Why are there so many fundamental particles, especiallywhen it seems that the great majority of things in the world aroundus need only electrons, up-quarks, and down-quarks? Why are there threefamilies? Why not one family or four families or any other number? Whydo the particles have a seemingly random spread of masses--why, for instance,does the tau weigh about 3,520 times as much as an electron? Whydoes the top quark weigh about 40,200 times as much an up-quark? Theseare such strange, seemingly random numbers. Did they occur by chance,by some divine choice, or is there a comprehensible scientific explanationfor these fundamental features of our universe?
| Family 1 | Family 2 | Family 3 |
|---|
| Particle | Mass | Particle | Mass | Particle | Mass |
|---|
| Electron | .00054 | Muon | .11 | Tau | 1.9 |
Electron-
neutrino | < 10-8 | Muon-
neutrino | < .0003 | Tau-
neutrino | < .033 |
| Up-quark | .0047 | Charm Quark | 1.6 | Top Quark | 189 |
| Down-quark | .0074 | Strange Quark | .16 | Bottom Quark | 5.2 |
Table 1.1 The three families of fundamental particles and their masses (in multiples of the proton mass). The values of the neutrino masses have so far eluded experimental determination.
The Forces, or, Where's the Photon?
Things only become more complicated when we consider the forces of nature.The world around us is replete with means of exerting influence: ballscan be hit with bats, bungee enthusiasts can throw themselves earthwardfrom high platforms, magnets can keep superfast trains suspended justabove metallic tracks, Geiger counters can tick in response to radioactivematerial, nuclear bombs can explode. We can influence objects by vigorouslypushing, pulling, or shaking them; by hurling or firing other objectsinto them; by stretching, twisting, or crushing them; or by freezing, heating,or burning them. During the past hundred years physicists have accumulatedmounting evidence that all of these interactions betweenvarious objects and materials, as well as any of the millions upon millionsof others encountered daily, can be reduced to combinations of four fundamentalforces. One of these is the gravitational force. The other three arethe electromagnetic force, the weak force, and the strongforce.
Gravity is the most familiar of the forces, being responsible for keepingus in orbit around the sun as well as for keeping our feet firmly plantedon earth. The mass of an object measures how much gravitational force itcan exert as well as feel. The electromagnetic force is the next most familiarof the four. It is the force driving all of the conveniences of modernlife--lights, computers, TVs, telephones--and underlies the awesomemight of lightning storms and the gentle touch of a human hand. Microscopically,the electric charge of a particle plays the same role for the electromagneticforce as mass does for gravity: it determines how strongly theparticle can exert as well as respond electromagnetically.
The strong and the weak forces are less familiar because their strengthrapidly diminishes over all but subatomic distance scales; they are thenuclear forces. This is why these two forces were discovered only muchmore recently. The strong force is responsible for keeping quarks "glued"together inside of protons and neutrons and keeping protons and neutronstightly crammed together inside atomic nuclei. The weak force isbest known as the force responsible for the radioactive decay of substancessuch as uranium and cobalt.
During the past century, physicists have found two features commonto all these forces. First, as we will discuss in Chapter 5, at a microscopiclevel all the forces have an associated particle that you can think of asbeing the smallest packet or bundle of the force. If you fire a laser beam--an"electromagnetic ray gun"--you are firing a stream of photons, thesmallest bundles of the electromagnetic force. Similarly, the smallestconstituents of weak and strong force fields are particles called weak gaugebosons and gluons. (The name gluon is particularlydescriptive: You can think of gluons as the microscopic ingredient in the strongglue holding atomic nuclei together.) By 1984 experimenters had definitivelyestablished the existence and the detailed properties of these three kinds offorce particles, recorded in Table 1.2. Physicists believe that thegravitational force also has an associated particle--the graviton--but itsexistence has yet to be confirmed experimentally.
The second common feature of the forces is that just as mass determineshow gravity affects a particle, and electric charge determines howthe electromagnetic force affects it, particles are endowed with certainamounts of "strong charge" and "weak charge" that determine how they areaffected by the strong and weak forces. (These properties are detailed inthe table in the endnotes to this chapter.) But as with particle masses, beyondthe fact that experimental physicists have carefully measured theseproperties, no one has any explanation of why our universe is composed ofthese particular particles, with these particular masses and force charges.
| Force | Force particle | Mass |
|---|
| Strong | Gluon | 0 |
| Electromagnetic | Photon | 0 |
| Weak | Weak gauge bosons | 86, 97 |
| Gravity | Graviton | 0 |
Table 1.2 The four forces of nature, together with their associated force particles and their masses in multiples of the proton mass. (The weak force particles come in varieties with the two possible masses listed. Theoretical studies show that the graviton should be massless.)
Notwithstanding their common features, an examination of the fundamentalforces themselves serves only to compound the questions. Why,for instance, are there four fundamental forces? Why not five or three orperhaps only one? Why do the forces have such different properties? Whyare the strong and weak forces confined to operate on microscopic scaleswhile gravity and the electromagnetic force have an unlimited range ofinfluence? And why is there such an enormous spread in the intrinsicstrength of these forces?
To appreciate this last question, imagine holding an electron in your lefthand and another electron in your right hand and bringing these two identicalelectrically charged particles close together. Their mutual gravitationalattraction will favor their getting closer while their electromagneticrepulsion will try to drive them apart. Which is stronger? There is no contest:The electromagnetic repulsion is about a million billion billion billionbillion (1042) times stronger! If your right bicep represents thestrength of the gravitational force, then your left bicep would have to extendbeyond the edge of the known universe to represent the strength of theelectromagnetic force. The only reason the electromagnetic force does notcompletely overwhelm gravity in the world around us is that most things arecomposed of an equal amount of positive and negative electric chargeswhose forces cancel each other out. On the other hand, since gravity is alwaysattractive, there are no analogous cancellations--more stuff meansgreater gravitational force. But fundamentally speaking, gravity is an extremelyfeeble force. (This fact accounts for the difficulty in experimentallyconfirming the existence of the graviton. Searching for the smallestbundle of the feeblest force is quite a challenge.) Experiments also haveshown that the strong force is about one hundred times as strong as theelectromagnetic force and about one hundred thousand times as strong asthe weak force. But where is the rationale--the raison d'etre--for ouruniverse having these features?
This is not a question borne of idle philosophizing about why certaindetails happen to be one way instead of another; the universe would be avastly different place if the properties of the matter and force particleswere even moderately changed. For example, the existence of the stablenuclei forming the hundred or so elements of the periodic table hingesdelicately on the ratio between the strengths of the strong and electromagneticforces. The protons crammed together in atomic nuclei all repel oneanother electromagnetically; the strong force acting among their constituentquarks, thankfully, overcomes this repulsion and tethers the protonstightly together. But a rather small change in the relative strengths ofthese two forces would easily disrupt the balance between them, andwould cause most atomic nuclei to disintegrate. Furthermore, were themass of the electron a few times greater than it is, electrons and protonswould tend to combine to form neutrons, gobbling up the nuclei of hydrogen(the simplest element in the cosmos, with a nucleus containing asingle proton) and, again, disrupting the production of more complex elements.Stars rely upon fusion between stable nuclei and would not formwith such alterations to fundamental physics. The strength of the gravitationalforce also plays a formative role. The crushing density of matterin a star's central core powers its nuclear furnace and underlies the resultingblaze of starlight. If the strength of the gravitational force were increased,the stellar clump would bind more strongly, causing a significantincrease in the rate of nuclear reactions. But just as a brilliant flareexhausts its fuel much faster than a slow-burning candle, an increase in thenuclear reaction rate would cause stars like the sun to burn out far morequickly, having a devastating effect on the formation of life as we know it.On the other hand, were the strength of the gravitational force significantlydecreased, matter would not clump together at all, thereby preventing theformation of stars and galaxies.
We could go on, but the idea is clear: the universe is the way it is becausethe matter and the force particles have the properties they do. Butis there a scientific explanation for why they have these properties?
String Theory: The Basic Idea
String theory offers a powerful conceptual paradigm in which, for the firsttime, a framework for answering these questions has emerged. Let's firstget the basic idea.
The particles in Table 1.1 are the "letters" of all matter. Just like theirlinguistic counterparts, they appear to have no further internal substructure.String theory proclaims otherwise. According to string theory, if wecould examine these particles with even greater precision--a precisionmany orders of magnitude beyond our present technological capacity--wewould find that each is not pointlike, but instead consists of a tinyonedimensional loop. Like an infinitely thin rubber band, each particlecontains a vibrating, oscillating, dancing filament that physicists, lackingGell-Mann's literary flair, have named a string. In Figure 1.1 weillustrate this essential idea of string theory by starting with an ordinarypiece of matter, an apple, and repeatedly magnifying its structure to reveal itsingredients on ever smaller scales. String theory adds the new microscopic layerof a vibrating loop to the previously known progression from atoms throughprotons, neutrons, electrons and quarks.
Although it is by no means obvious, we will see in Chapter 6 that thissimple replacement of point-particle material constituents with stringsresolves the incompatibility between quantum mechanics and general relativity.String theory thereby unravels the central Gordian knot of contemporarytheoretical physics. This is a tremendous achievement, but it isonly part of the reason string theory has generated such excitement.
String Theory as the Unified Theory of Everything
In Einstein's day, the strong and the weak forces had not yet been discovered,but he found the existence of even two distinct forces--gravity andelectromagnetism--deeply troubling. Einstein did not accept that natureis founded on such an extravagant design. This launched his thirty-yearvoyage in search of the so-called unified field theory that he hopedwould show that these two forces are really manifestations of one grandunderlying principle. This quixotic quest isolated Einstein from the mainstreamof physics, which, understandably, was far more excited about delving intothe newly emerging framework of quantum mechanics. He wrote to afriend in the early 1940s, "I have become a lonely old chap who is mainlyknown because he doesn't wear socks and who is exhibited as a curiosityon special occasions."
Einstein was simply ahead of his time. More than half a century later,his dream of a unified theory has become the Holy Grail of modernphysics. And a sizeable part of the physics and mathematics communityis becoming increasingly convinced that string theory may provide the answer.From one principle--that everything at its most microscopic levelconsists of combinations of vibrating strands--string theory provides asingle explanatory framework capable of encompassing all forces and allmatter.
String theory proclaims, for instance, that the observed particle properties,the data summarized in Tables 1.1 and 1.2, are a reflection of thevarious ways in which a string can vibrate. Just as the strings on a violinor on a piano have resonant frequencies at which they prefer to vibrate--patternsthat our ears sense as various musical notes and their higherharmonics--the same holds true for the loops of string theory. But wewill see that, rather than producing musical notes, each of the preferredpatterns of vibration of a string in string theory appears as a particle whosemass and force charges are determined by the string's oscillatory pattern.The electron is a string vibrating one way, the up-quark is a string vibratinganother way, and so on. Far from being a collection of chaotic experimentalfacts, particle properties in string theory are the manifestation ofone and the same physical feature: the resonant patterns of vibration--themusic, so to speak--of fundamental loops of string. The same idea appliesto the forces of nature as well. We will see that force particles are alsoassociated with particular patterns of string vibration and hence everything,all matter and all forces, is unified under the same rubric of microscopicstring oscillations--the "notes" that strings can play.
For the first time in the history of physics we therefore have a frameworkwith the capacity to explain every fundamental feature upon whichthe universe is constructed. For this reason string theory is sometimesdescribed as possibly being the "theory of everything" (T.O.E.) or the"ultimate" or "final" theory. These grandiose descriptive terms are meant tosignify the deepest possible theory of physics--a theory that underlies allothers, one that does not require or even allow for a deeper explanatorybase. In practice, many string theorists take a more down-to-earth approachand think of a T.O.E. in the more limited sense of a theory thatcan explain the properties of the fundamental particles and the propertiesof the forces by which they interact and influence one another. Astaunch reductionist would claim that this is no limitation at all, and thatin principle absolutely everything, from the big bang to daydreams, canbe described in terms of underlying microscopic physical processes involvingthe fundamental constituents of matter. If you understand everythingabout the ingredients, the reductionist argues, you understandeverything.
The reductionist philosophy easily ignites heated debate. Many find itfatuous and downright repugnant to claim that the wonders of life and theuniverse are mere reflections of microscopic particles engaged in a pointlessdance fully choreographed by the laws of physics. Is it really the casethat feelings of joy, sorrow, or boredom are nothing but chemical reactionsin the brain--reactions between molecules and atoms that, even moremicroscopically, are reactions between some of the particles in Table 1.1,which are really just vibrating strings? In response to this line of criticism,Nobel laureate Steven Weinberg cautions in Dreams of a Final Theory,
At the other end of the spectrum are the opponents of reductionism who are appalled by what they feel to be the bleakness of modern science. To whatever extent they and their world can be reduced to a matter of particles or fields and their interactions, they feel diminished by that knowledge.... I would not try to answer these critics with a pep talk about the beauties of modern science. The reductionist worldview is chilling and impersonal. It has to be accepted as it is, not because we like it, but because that is the way the world works.
Some agree with this stark view, some don't.
Others have tried to argue that developments such as chaos theory tellus that new kinds of laws come into play when the level of complexity ofa system increases. Understanding the behavior of an electron or a quarkis one thing; using this knowledge to understand the behavior of a tornadois quite another. On this point, most agree. But opinions diverge onwhether the diverse and often unexpected phenomena that can occur insystems more complex than individual particles truly represent new physicalprinciples at work, or whether the principles involved are derivative,relying, albeit in a terribly complicated way, on the physical principlesgoverning the enormously large number of elementary constituents. Myown feeling is that they do not represent new and independent laws ofphysics. Although it would be hard to explain the properties of a tornadoin terms of the physics of electrons and quarks, I see this as a matter ofcalculational impasse, not an indicator of the need for new physical laws.But again, there are some who disagree with this view.
What is largely beyond question, and is of primary importance to thejourney described in this book, is that even if one accepts the debatablereasoning of the staunch reductionist, principle is one thing and practicequite another. Almost everyone agrees that finding the T.O.E. would in noway mean that psychology, biology, geology, chemistry, or even physics hadbeen solved or in some sense subsumed. The universe is such a wonderfullyrich and complex place that the discovery of the final theory, inthe sense we are describing here, would not spell the end of science.Quite the contrary: The discovery of the T.O.E.--the ultimate explanationof the universe at its most microscopic level, a theory that does not rely onany deeper explanation--would provide the firmest foundation on whichto build our understanding of the world. Its discovery would mark abeginning, not an end. The ultimate theory would provide an unshakable pillarof coherence forever assuring us that the universe is a comprehensibleplace.
The State of String Theory
The central concern of this book is to explain the workings of the universeaccording to string theory, with a primary emphasis on the implicationsthat these results have for our understanding of space and time. Unlikemany other exposes of scientific developments, the one given here doesnot address itself to a theory that has been completely worked out, confirmedby vigorous experimental tests, and fully accepted by the scientificcommunity. The reason for this, as we will discuss in subsequent chapters,is that string theory is such a deep and sophisticated theoretical structurethat even with the impressive progress that has been made over the lasttwo decades, we still have far to go before we can claim to have achievedfull mastery.
And so string theory should be viewed as a work in progress whose partialcompletion has already revealed astonishing insights into the nature ofspace, time, and matter. The harmonious union of general relativity andquantum mechanics is a major success. Furthermore, unlike any previoustheory, string theory has the capacity to answer primordial questions havingto do with nature's most fundamental constituents and forces. Ofequal importance, although somewhat harder to convey, is the remarkableelegance of both the answers and the framework for answers that stringtheory proposes. For instance, in string theory many aspects of nature thatmight appear to be arbitrary technical details--such as the number of distinctfundamental particle ingredients and their respective properties--arefound to arise from essential and tangible aspects of the geometry ofthe universe. If string theory is right, the microscopic fabric of our universeis a richly intertwined multidimensional labyrinth within which the stringsof the universe endlessly twist and vibrate, rhythmically beating out thelaws of the cosmos. Far from being accidental details, the properties ofnature's basic building blocks are deeply entwined with the fabric of spaceand time.
In the final analysis, though, nothing is a substitute for definitive,testable predictions that can determine whether string theory has trulylifted the veil of mystery hiding the deepest truths of our universe. It maybe some time before our level of comprehension has reached sufficientdepth to achieve this aim, although, as we will discuss in Chapter 9,experimental tests could provide strong circumstantial support for stringtheory within the next ten years or so. Moreover, in Chapter 13 we will seethat string theory has recently solved a central puzzle concerning blackholes, associated with the so-called Bekenstein-Hawking entropy, that hasstubbornly resisted resolution by more conventional means for more thantwenty-five years. This success has convinced many that string theory isin the process of giving us our deepest understanding of how the universeworks.
Edward Witten, one of the pioneers and leading experts in string theory,summarizes the situation by saying that "string theory is a part oftwenty-first-century physics that fell by chance into the twentieth century,"an assessment first articulated by the celebrated Italian physicist DanielleAmati. In a sense, then, it is as if our forebears in the late nineteenthcentury had been presented with a modern-day supercomputer, without theoperating instructions. Through inventive trial and error, hints of thesupercomputer's power would have become evident, but it would have takenvigorous and prolonged effort to gain true mastery. The hints of the computer'spotential, like our glimpses of string theory's explanatory power,would have provided extremely strong motivation for obtaining completefacility. A similar motivation today energizes a generation of theoreticalphysicists to pursue a full and precise analytic understanding of stringtheory.
Witten's remark and those of other experts in the field indicate that itcould be decades or even centuries before string theory is fully developedand understood. This may well be true. In fact, the mathematics of stringtheory is so complicated that, to date, no one even knows the exact equationsof the theory. Instead, physicists know only approximations to theseequations, and even the approximate equations are so complicated thatthey as yet have been only partially solved. Nevertheless, an inspiring setof breakthroughs in the latter half of the 1990s--breakthroughs that haveanswered theoretical questions of hitherto unimaginable difficulty--maywell indicate that complete quantitative understanding of string theory ismuch closer than initially thought. Physicists worldwide are developingpowerful new techniques to transcend the numerous approximate methodsso far used, collectively piecing together disparate elements of thestring theory puzzle at an exhilarating rate.
Surprisingly, these developments are providing new vantage points forreinterpreting some of the basic aspects of the theory that have been inplace for some time. For instance, a natural question that may have occurredto you in looking at Figure 1.1 is, Why strings? Why not little frisbeedisks? Or microscopic bloblike nuggets? Or a combination of all ofthese possibilities? As we shall see in Chapter 12, the most recent insightsshow that these other kinds of ingredients do have an important rolein string theory, and have revealed that string theory is actually part of aneven grander synthesis currently (and mysteriously) named M-theory.These latest developments will be the subject of the final chapters of thisbook.
Progress in science proceeds in fits and starts. Some periods are filledwith great breakthroughs; at other times researchers experience dry spells.Scientists put forward results, both theoretical and experimental. Theresults are debated by the community, sometimes they are discarded,sometimes they are modified, and sometimes they provide inspirationaljumping-off points for new and more accurate ways of understanding thephysical universe. In other words, science proceeds along a zig-zag pathtoward what we hope will be ultimate truth, a path that began with humanity'searliest attempts to fathom the cosmos and whose end we cannotpredict. Whether string theory is an incidental rest stop along thispath, a landmark turning point, or in fact the final destination we do notknow. But the last two decades of research by hundreds of dedicatedphysicists and mathematicians from numerous countries have given uswell-founded hope that we are on the right and possibly final track.
It is a telling testament of the rich and far-reaching nature of stringtheory that even our present level of understanding has allowed us to gainstriking new insights into the workings of the universe. A central thread inwhat follows will be those developments that carry forward the revolutionin our understanding of space and time initiated by Einstein's special andgeneral theories of relativity. We will see that if string theory is correct,the fabric of our universe has properties that would likely have dazzled evenEinstein.
Continues...
Excerpted from The Elegant Universeby Brian Greene Copyright © 2000 by Brian Greene. Excerpted by permission.
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