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New Scientist 9 February 1984 31

The eleven dimensions of realityTheoretical physicists are beginning to piece together a unified theory of the Universe.But they picture a strange world in which force and matter are abolished and becomemerelyknots and kinks in the II-dimensional geometry of space-time

Paul DaviesAN AGE-OLD scientific dream isJ-\..that the physical world mightbe reducible, ultimately, to puregeometry;that what we seeasmaterialbodiesand forcesarenothing but knotsand kinks in empty space-time. Theidea has an appealing economy toit-the concrete substantiality of theworld whipped out of a frolic ofnothingness.The first serious step in thegeometrisationof nature was taken byAlbertEinstein in his general theory ofrelativity, published in 1915. In thishistoric work, Einstein abolished theforceofgravity;replacingit by an enig-matic fieldof geometrical distortion, awarping, or curving, of space-time.Accordingto general relativity, bodiesarenot pulledby forcesofgravityat all,as Newton had claimed centuriesbefore.They simplymeander as effort-lessly as possible through an under-lying warped space-time. Viewed thisway,the curvature of the Earth's orbitaround the Sun is not really due to aforce of gravity, but is a reflection ofthe curvature of space-time in theSun's vicinity. (In spite of this, phys-icists still find it convenient tocontinue referring to "the force ofgravity".)The p..Qwer and elegance ofEinstein's geometrical description ofgravity soon inspired a little-knownPolish physicist, Theodor Kaluza, tolook for a more comprehensivegeometrisation of nature. In 1921Kaluza published an extension ofEinstein's general relativity in which he claimed that bothgravity and electromagnetism could be formulated ingeometricallanguage;provided they wereunited into a singlefield theory. Kaluza's was the first attempt at a unified fieldtheory, and it seemed to be something of a mathematicalmiracle. Kaluza showed that electromagnetism can beregarded as a form of gravity-and here was the bizarretwist""7"thegravity of a fifth dimension. .The ordinary space of our perceptions is, of course, three-dimensional. Relativity links.space and time, so physicistshave traditionally thought of the world as four-dimensional,three dimensions of spaceplus one of time. Kaluza proposedthat there exists yet another dimension of space-a fifthspace-timedimension-that wedo not see.Accordingto thistheory, what we interpret as electromagnetism is, in roughterms, gravity acting in this unseen fifth dimension. Thetheory abolishes electromagnetic forces, just as Einsteindisposedof gravitational forces,and replacesthem bywarpedgeometry, this time five-dimensional geometry. In Kaluza'stheory, an electromagneticwave, such as a radio wave,is aripple in the fifth dimension. The most remarkable feature ofthe theory is that Einstein's gravitational field equations,when extended to five dimensions, should reproduce exactly

the laws of gravity and electro-magnetism in the four space-timedimensions of direct experience.The chief weakness of Kaluza'soriginaltheory isthat wedo not seethisextra dimension of spacewhichplays acentral role in the description of elec-tromagnetism. Where is it?In 1926the SwedishphysicistOskarKlein came to the rescueby suggestingthat we do not see Kaluza's fifthdimension because it is shrunken toinvisibility. The situation can becompared to viewingahosepipe from adistance. What from afar looks like awigglyone-dimensional line, on closerscrutiny, turns out to bea narrowtube.Every point on the "line" is, in fact, alittle circle around the circumferenceof the tube. Klein proposed,. anal-ogously, that what superficiallyappears to be a single, structurelesspoint in space,is in reality a tiny circlegoing around the fifth dimension. Wedo not notice the extra dimensionof space because it has been"compactified", or rolledup on itselftoa very small size. Calculations put thecircumferenceofthis "tube" ofspaceatabout twenty powers of ten smallerthan an atomic nucleus-far too smallfor us to have discerned it directly,even in sub-nuclear particle experi-ments.The Kaluza-Klein theory, thoughintriguing, remained littlemore than acuriosity for several decades. It wasdiscussed in detail by Stephen Unwinin "Living in a five-dimensionalworld",NewScientist, 29April 1982,p 296. Sincethen, therehas been a surge of renewed interest occasioned by somespectacular recent developments in the search for a unifiedfield theory.Today,physicistsrecognisenot two, but four basicforcesofnature. In addition to gravity and electromagnetism, twqnuclear forces,calledweakand strong, have alsobeen discov-

ered. Any successful unified field theory would have toaccommodate these two nuclear forces as well. Significantprogressalong this road was achievedin the late 1960swhenSteven Weinberg and Abdus Salam found a mathematicaldescription that weaves together electromagnetism and theweak force into a single conceptual scheme. Physicistsconsider this a major advance in our understanding of therelationship between the different forcesof nature.During,the 1970s,suggestionsfor further unification camefrom Sheldon Glashowand others, in which the strongforceis mergedwith the newlyunified electromagnetic-weakforcein what have become known as "grand unified theories", orGUTs for short.The aim ofthe GUTs isto provide a unitarymathematical framework in which three out of four ofnature's forces emerge as closely related components. Thetheorist's ability to subsume three apparently very different

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32-sorts 'Offorcesunder a singleconceptual umbrella hingeson the discovery that theseforces can all be describedusing so-called"gaugefields". inwhichcertainabstract,butdistinctive,symmetriesoccurin the structure of the forcefields. The presence of thesecrucial symmetries alreadyhints that some sort of hid-den geometry is at work inthe operation of the forcesofnature. Only in the pastcouple of years has thisgeometry been made fullyexplicit-by appealing to thei~ea of further.space dimen-SIOnsonce agaIn.In the Kaluza-Kleintheory, electromagnetismwasembodied within gravityby grafting a single extradimension onto fout-dimensional space-time. Ex-tending their theory toincorporate the trio of forces-electromagnetism, weakand strong-demands stillmore dimensions of space.The weak and strongforces are more complicatedin structure than. electro-magnetism. For example,whereas the photon can beregarded as the "messenger"that transmits the electro-magnetic forcebetween elec-trically charged particles, theequivalent quantum descrip-ti~m of the weak forcedemands both the newlydiscovered Z particle, whichis identical to a photon ineverythingexceptmass,and two electricallycharged messen-gerscalledW+and W-. When it comes to the strongforce, nofewerthan eightsorts ofmessengerquanta (knownasgluons)are needed. To accommodate all this additional complexity,the Kaluza-Kleintheory has to be enlargedto involve a totalofsevenextraspacedimensions,making iOspacedimensionsplus time, or ii space-time dimensions in all.Is it conceivablethat theUniverse reallyis ii-dimensional,and that what wehave alwaysregarded as forcesare actuallythe unseen seven dimensions at work?One man who thinksso isMichael Duff ofImperial College,London, whowith hiscolleague Chris Pope has been developing the eleven-dimensional Kaluza-Klein theory for a couple of years.In this challenging task, intuition is of little help. Higher-dimensional spaces leave the imagination floundering. Onthe other hand, mathematics has no need of visualisation,and mathematicians routinely study all manner. of multi-dimensional spaces for their interesting properties. Onesuch was Elie Cartan, a French mathematician, who in thei920s elucidated many of the geometrical properties ofmulti-dimensional spaces. Cartan's work, while conductedpurely for its intrinsic interest, is turning out to have anunforeseen importance in the revitalised Kaluza-Kleintheory.As in the original version of the theory, it is necessarytoassume that the extra dimensions are compactified, that is,rolled up somehow to a microscopic size. When only oneadditional dimension of space was involved, this

New Scientist 9 February 1984

compactification meant regarding each point in three-dimensional space as a tiny circle. In the extended theory,each point becomes a seven-dimensionalcompact space,andthere are a great many different ways to compactify sevendimensions.Remarkably, however, one particular choice stands apart.-This is the seven-dimensionalanalogue of the sphere, knownfor short as the seven sphere. Cartan and other mathe-maticians had demonstrated that the seven sphere ispossessedof a number of unique geometrical properties: andthese, moreover, are precisely the properties required if theextra dimensions are to be interpreted as force fields.A sphere is a highly symmetric shape, and a seven sphereembodies many additional powerful symmetries that reflectthe all-important gauge symmetries on which our presentdescription of the forces of nature hinges. However, one ofthe reasons it took so long for physiciststo understand theseforcesis that, under most circumstances, the symmetries arehidden, or broken. This symmetry-breaking may bereproduced in the Kaluza-Kleintheory by allowingthe sevensphere to be slightly distorted, or squashed. The squashedseven sphere is emergingas the most favoured shape for theunseen dimensions of space.The new Kaluza-Klein theory has proved so inspiring totheoretical physiciststhat they have been rushing to adapt allthe laws of physics from 4 to il dimensions. One obviousproblem to be tackled is to find a reason why anii-dimensional space--timeshould arrange itself irito four

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New Scientist 9 February 1984 33plus seven. The hope is thatthis configurationrepresents,in some sense, the lowestenergystate of space-time.Inphysics, systems generallyseekout a state ofminimumenergy, so it is possible tobelieve that when theuniverse was created, all 10dimensions of space existedon a.nequal footing, but thatsomehow seven of themspontaneously decayed,curl-ingup into a shrunken ball. Ifthe idea is correct, it opensup a tantalising possibility.Perhaps the unstable sevendimensions remained activefor longenough in the prime-val cosmos to leave animprint on the structure ofthe universe, an imprint thatremains to this day?The most spectacular suchpossibility is that the seven. vanished. dimensions willprovide an explanation forthe big bang itself. The ulti-mate cosmic mystery is thecause of the explosionwhichbrought the physical Uni-verse into being about 15billion years ago. The onlyforce known to us that cantake control of the entireUnh,erse is gravity,but in allQur experience gravity isattractive-it is a pullingforce.The explosiveoutburst-which marked the creation of~theUniverse requiresa push-

~ ing force of unimaginable power to blast the cosmicfragments apart and set theUniverse on the path of expansion. Very recently, theoristshave discovered that unified,force fields naturally tend toproduce just such a repulsive force under the extreme condi-tions expected in the big bang.One conceivable scenario for the creation goes somethinglike this: In the beginning, II-dimensional space-time erup-ted spontaneously out of literally nothing, an event that isonly explicablewithinthe context of quantum physics,whichpermits the uncaused creation of physical structures. Theshapeof space need not initially have been speciallyordered;it could have been chaotic and turbulent. In some regions,inevitably, the configuration would have been such that thecompetition of forcesproduced a huge repulsion. Asa result,three space dimensions began to expand at an acceleratingrate, while the remaining dimensions spontaneously rolledthemselvesinto a seven sphere. If the outward driving forcecould sustain itself for long enough, the explosive violencecharacteristic of the big bang would be achieved.At this stage such ideas can only be tested by calculation.Would the repulsiveforcehave lastedlong enough?Is it inev-itable that three dimensions ofspaceembark upon expansionwhile seven collapse, or could there be a different split, say,two plus eight? .It may be that even the number of starting dimensions isvariable,and that 11 has been selected a.nthropicallytoo.There is, however, some curious independent evidence thatsuggests.the.number 11is unique. It comes from a branch ofphysics which sets as its goal the formulation of a mathe-

matically consistent quantum theory of gravity. For sometime, physicistshave been greatly distressed that the generaltheory ofrelativity,whateverits intrinsicmerits,clashesbadlywith the principles of quantum physics.The onlyway out ofthis impasse seemsto be to embed general relativityin amorecomprehensive theory of gravity which involves extracomponents- types of gravity we haven't yet seen. Accord-ing to this philosophy, all the mathematical troubles withquantum gravity have arisen because physicists have beenartificiallyisolatingwhat is actuallyonly a fragment ofthe fullpanoply of gravitational forces.To achievea completetheory ofgravity-one whichwillbeconsistent with quantum physics-the gravitational force offamiliar experiencehas to be fittedtogether snugly(ina math-ematical sense)with the additional, as yet undetected, grav-itational components. For the past decade, an army oftheoristshas been engagedon this daunting enterprise. Theirwork has centred on a key idea, called supersymmetry. Thisis an abstract mathematical concept related to thephenomenon of intrinsic spin found among subatomicparticles.The technical details do not matter here. The pointis that the most elegant formulation of a supersymmetrictheory of gravity is one in which space-time has 11 dimen-sions!Is this just an improbable coincidence, or does it pointcompellingly to a deep connection with the unified gaugetheories of the other three forces of nature? Is the mathe-matics hinting at a fullyunified fieldtheory, in which gravityand other forces are merged into a singlesuperforce?If so,then that age-old dream of building the world out of puregeometry could be close to realisation-but the geometrywould be that of an 11 dimensional universe. 0. Paul Davies is professor of theoretical physics at the University of.~Newcastle upon Tyne. His latest popular book is God and the NewPhysics (Dent).

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