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Home , Theoretical physics

The Future of Fundamental

Nima Arkani-Hamed

Abstract: Fundamental physics began the twentieth century with the twin revolutions of relativity and quantum , and much of the second half of the century was devoted to the con- struction of a theoretical structure unifying these radical ideas. But this foundation has also led us to a number of paradoxes in our understanding of nature. Attempts to make sense of and at the smallest distance scales lead inexorably to the conclusion that - Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 time is an approximate notion that must emerge from more primitive building blocks. Further- more, violent short-distance quantum fluctuations in the vacuum seem to make the existence of a macroscopic world wildly implausible, and yet we live comfortably in a huge . What, if anything, tames these fluctuations? Why is there a macroscopic universe? These are two of the central theoretical challenges of fundamental physics in the twenty-½rst century. In this essay, I describe the circle of ideas surrounding these questions, as well as some of the theoretical and experimental fronts on which they are being attacked.

Ever since Newton realized that the same force of gravity pulling down on an apple is also responsible for keeping the moon orbiting the , funda- mental physics has been driven by the program of uni½cation: the realization that seemingly disparate phenomena are in fact different aspects of the same underlying cause. By the mid-1800s, electricity and were seen as different aspects of elec- tromagnetism, and a seemingly unrelated phenom- enon––was understood to be the undulation of electric and magnetic ½elds. NIMA ARKANI-HAMED, a Fellow Relativity and quantum mechanics pushed the of the American Academy since trend toward uni½cation into territory far removed 2009, is a Professor in the School from ordinary human . Einstein taught of Natural at the Institute us that space and time are different aspects of a sin- for Advanced Study. His interests gle entity: space-time. and are range from quantum ½eld united analogously, leading to the famous equiva- and to cosmology and lence between and energy, E =mc2, as an im- collider physics. He has published his work in the Journal of High Ener- mediate consequence. Einstein further realized gy Physics, the Journal of Cosmology that space-time is not a static stage on which phys- and , and Nucle- ics unfolds, but a dynamic entity that can curve and ar Physics, among other places. bend. Gravity is understood as a manifestation of

© 2012 by the American Academy of Arts & Sciences

53 The Future space-time curvature. This new picture ways. The nature of the interactions is of Funda- of space-time made it possible to conceive almost completely dictated by the rules mental Physics of ideas that were impossible to articulate of quantum mechanics, together with the in the Newtonian picture of the world. requirement that the interactions take Consider the most important fact about place at points in space-time, in compli- cosmology: we live in an expanding uni- ance with the laws of . The verse. The distance between two galaxies latter requirement is known as the princi- grows with time. But the galaxies are not ple of locality. rushing apart from each other into some One of the startling general predictions preexisting space, as though blown out of of quantum ½eld theory is the existence of an explosion from some common center. anti-particles such as the positron, which

Rather, more and more space is being gen- has the same properties as the electron but Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 erated between the galaxies all the time, the opposite electric charge. This predic- so from the vantage point of any one gal- tion has another striking consequence: axy, the others appear to be rushing away. namely, that even the vacuum has struc- This picture, impossible to imagine in ture and . Newton’s universe, is an inevitable con- Suppose we attempt to check that some sequence of Einstein’s theory. small region of space-time is empty. Be- Quantum mechanics represented a more cause of the , we need radical departure from , higher to probe short distances. involving a completely new conceptual Eventually there is enough energy to make framework, both physically and mathe- an electron and a positron, without vio- matically. We learned that nature is not lating either the deterministic, and only probabilities can or the conservation of charge. Instead of be predicted. One consequence is the fa- seeing nothing, probing the vacuum at mous uncertainty principle, by which we small distances yields particle/anti-particle cannot simultaneously know the position pairs. It is useful to think of the vacuum and velocity of a particle to perfect accu- as ½lled with quantum fluctuations, with racy. Quantum mechanics also allowed “virtual” particles and anti-particles pop- previously irreconcilable phenomena to ping in and out of existence on faster and be understood in a uni½ed way: particles faster timescales at shorter and shorter and waves came to be seen as limiting as- distances. pects of the underlying description where These quantum fluctuations give rise to there are no waves at all, only quantum- measurable physical effects. For instance, mechanical particles. the cloud of virtual electrons and posi- trons surrounding an electron is slightly The laws of relativity and quantum perturbed by the electron’s electric ½eld. mechanics are the pillars of our current Any physical measurement of the elec- understanding of nature. However, de- tron’s charge, then, will vary just slightly scribing physics in a way that is compat- with distance, growing slowly closer in to ible with both of these principles turns the electron as more of the virtual cloud out to be extremely challenging; indeed, is pierced. These virtual effects can be cal- it is possible only with an extremely con- culated very precisely; in some circum- strained theoretical structure, known as stances, theoretical predictions and exper- quantum ½eld theory. A quantum ½eld the- imental observations can be compared to ory is characterized by a menu of particles an astonishing level of precision. The vir- that interact with each other in various tual corrections to the magnetic proper-

54 Dædalus, the Journal ofthe American Academy of Arts & Sciences ties of the electron, for example, have been same quantum-½eld-theoretic language. Nima theoretically computed to twelve decimal is associated with inter- Arkani- Hamed places, and they agree with to actions between electrons and photons of that level of precision. a speci½c sort. Strong interactions arise The second-half of the twentieth cen- from essentially identical interactions be- tury saw a flurry of activity, on both ex- tween quarks and gluons, while weak inter- perimental and theoretical fronts. These actions connect particles like the electron developments culminated in the 1970s and the neutrino in the same way, with with the construction of the Standard massive cousins of the photon known as Model of , a speci½c quan- the W and Z particles. tum ½eld theory that describes all known Differences appear at long distances for

elementary particles and their interactions subtle reasons. The electromagnetic inter- Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 down to the smallest distances we have was the ½rst to be detected and un- probed so far. There are four basic inter- derstood because the photon is massless actions: gravity and electromagnetism, and the interaction is long-ranged. The W which were familiar even to the ancients, and Z particles are massive, thus mediat- as well as the weak and strong interactions ing an interaction with a short range of that reveal themselves only on nuclear about 10-17 cm. The difference with quarks scales. Atomic nuclei consist of neutrons and gluons is more subtle still: the virtual and protons. An isolated neutron is un- effects of the cloud of gluons surround- stable, living for about ½fteen minutes be- ing a quark make the “strong charge” of fore disintegrating into a proton, electron, quarks slowly grow stronger at longer dis- and an anti-neutrino. (This process is also tances. At a distance of roughly 10-14 cm, responsible for radioactivity.) Fifteen min- the interaction is so strong as to perma- utes is enormously long compared to the nently con½ne quarks inside protons and typical timescales of and nuclei, so neutrons. the interaction responsible for triggering But from a fundamental short-distance this decay must be very feeble–hence, perspective, these are details: the character . The earliest incarnation of the laws is essentially identical. This of the strong interaction was noticed in the fact illustrates the central reason why we attraction keeping protons inside nuclei, probe short distances in fundamental counterbalancing their huge electrical re- physics. It is not so much because we care pulsion. about the “building blocks of ” and Some familiar particles, such as elec- the associated set of particles we may dis- trons and photons, remain as elementary cover, but because we have learned that point-like entities in the . the essential unity, simplicity, and beauty Others, like the proton, are understood to of the underlying laws manifest most be bound states, around 10-14 cm in diam- clearly at short distances. eter made of quarks, which are perma- The Standard Model is one of the tri- nently trapped inside the proton through umphs of physics in the twentieth century. their interaction with gluons. It gives us a simple and quantitatively ac- Strong, weak, and electromagnetic inter- curate description of we know actions seem completely different from about elementary particles and their inter- each other at long distances, but we now actions. Only one element of the theory has know that these differences are a long- yet to be de½nitely con½rmed by experi- distance illusion. At short scales, these in- ment. In the fundamental short-distance teractions are described in essentially the theory, where all the interactions are treat-

141 (3) Summer 2012 55 The Future ed on a symmetrical footing, the particles time is necessarily an approximate notion of Funda- are massless. The mass of particles, such that must emerge from more primitive mental W Z Physics as electrons or the and particles, arises building blocks. as a dynamic long-distance effect, known Because of the uncertainty principle, we as the Higgs mechanism because of the have to use high energies to probe short particles’ interactions with the so-called distances. In a world without gravity, we Higgs ½eld. The typical length scale asso- could resolve arbitrarily small distances in ciated with these interactions is around this way, but gravity eventually and dra- 10-17 cm, which is, not coincidentally, also matically changes the picture. At minis- the range of weak interactions. As I discuss cule distances, so much energy has to be at greater length below, it is also fortu- concentrated into such a tiny region of

itously the distance scale we are now prob- space that the region itself collapses into Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 ing with the Large Hadron Collider (lhc), a black hole, making it impossible to ex- the particle accelerator located at the cern tract any information from the experiment. laboratory just outside Geneva, Switzer- This occurs when we attempt to probe land. Collisions at the lhc should put rip- distances around 10-33 cm, the so-called ples in the Higgs ½eld that manifest as the . Higgs particle with very de½nite proper- The Planck length is a ridiculously tiny ties and experimental signatures. Indeed, distance scale–sixteen orders of magni- last December, the lhc re- tude smaller than the tiniest distances we ported preliminary evidence for events are probing today at the lhc. Its tininess consistent with the production of the is a direct reflection of the extreme weak- Higgs particle, with its expected prop- ness of gravity compared to other forces erties. Analysis of the 2012 data should of nature. The gravitational attraction be- either yield a de½nitive discovery of the tween a pair of electrons is forty-two orders Higgs particle or de½nitively exclude the of magnitude smaller than their electrical simplest realization of the Higgs mecha- repulsion. Classically, both the gravitation- nism within the Standard Model. al and electric forces vary with distance The success of the Standard Model gives following an inverse-square law; however, us a strong indication that we are headed at a distance of around 10-11 cm, this gets in the right direction in our understand- corrected in an important way: again be- ing of fundamental physics. Yet profound cause of the uncertainty principle, simply mysteries remain, associated with ques- holding two electrons at shorter distances tions that either lie outside the scope of the requires a huge amount of energy. The Standard Model or are addressed by it, but force of gravity increases with increasing in a seemingly absurd way. Two of these mass, or with equivalently increasing en- questions stand out for both their sim- ergy, so the attraction between electrons plicity and urgency, and will drive the de- begins to increase relative to the electri- velopment of fundamental physics in the cal repulsion. At around 10-31 cm, gravity twenty-½rst century. surpasses the electric force, and at 10-33 cm, it dominates all interactions. The principle of locality–the notion that Thus, the combination of gravity and interactions take place at points in space- quantum mechanics makes it impossible time–is one of the two pillars of quan- to operationally probe Planckian dis- tum ½eld theory. It is therefore unsettling tances. Every time we have encountered to realize that, due to the effects of both ideas in physics that cannot even in prin- gravity and quantum mechanics, space- ciple be observed, we have come to see such

56 Dædalus, the Journal ofthe American Academy of Arts & Sciences ideas as approximate notions. However, tum fluctuations, and therefore cannot Nima this instance is particularly disturbing be- record the results of the experiment with Arkani- Hamed cause the notion that emerges as approx- perfect accuracy. Without gravity, noth- imate is that of space-time itself. ing would stop us from conducting the The description of the situation seems experiment with an in½nitely big appara- to relegate all the mysteries to tiny dis- tus to achieve perfect accuracy, but grav- tances, and may suggest some sort of gran- ity obstructs this. As the apparatus gets ular structure to space-time near the bigger, it inevitably also gets heavier. If Planck scale. Much as the smooth surface we are making a local measurement in a of a table is resolved into discrete units ½nite-sized room, at some large but ½nite made of and atoms, one might size it becomes so heavy that it collapses

imagine that “atoms of space-time” will the entire room into a black hole. Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 replace space-time near the Planck length. This means that there is no way, not This naive idea is very likely wrong. Any even in principle, to make perfectly accu- sort of granular structure to space-time rate local measurements, and thus local ob- picks a of reference, where servables cannot have a precise meaning. the size of the granularity is “small,” in There is an irreducible error associated sharp conflict with the laws of relativity. with any local measurement that is made But there is a deeper reason to suspect in a ½nite room. While this error is signi½- that something much more interesting and cant close to the Planck scale, it is negligi- subtle than “atoms of space-time” is at ble in ordinary circumstances. But this play. The problems with space-time are not does not diminish the importance of this only localized to small distances; in a pre- observation. The fact that quantum me- cise sense, “inside” regions of space-time chanics makes it impossible to determine cannot appear in any fundamental descrip- precisely the position and velocity of a tion of physics at all. baseball is also irrelevant to a baseball The slogan is that due to quantum me- player. However, it is of fundamental im- chanics and gravity, there are no “local portance to physics that we cannot speak observables.” Indeed, before worrying precisely of position and momentum, but about what a correct theory combining only position or momentum. Similarly, the quantum mechanics and gravity ought to fact that gravity makes it impossible to look like, it is worth thinking about what have precise local observables has the dra- perfectly precise measurements can ever matic consequence that the “inside” of be made by experiments. These (in prin- any region of space-time does not have a ciple) exact observables provide a target sharp meaning, and is likely an approxi- for what the theory should predict. mate notion that cannot appear in a deeper Imagine trying to perform any sort of underlying theory. local measurement, by which I mean an experiment that can be done in a ½nite- If we cannot speak precisely of local ob- sized room. To extract a perfectly precise servables, what observables can we talk measurement, we need (among other about? Instead of performing observa- things) to use an in½nitely large appara- tions inside some region of space-time, tus in order to avoid inaccuracies arising we can push our detectors out to in½nite from the quantum fluctuations of the ap- distances, at the boundary of space-time, paratus. If the apparatus has a large but where we can make them in½nitely big. ½nite number of components, on a huge We can then throw particles into the inte- but ½nite timescale, it suffers its own quan- rior, where they interact and scatter with

141 (3) Summer 2012 57 The Future each other in some way and emerge back into the interior of the box and watch them of Funda- out to in½nity where they are measured. come back out to the walls at some ½nite mental Physics The results of these scattering experiments time in the future. Because these experi- can be the perfectly precise observables ments start and end on the walls, it is nat- that one might hope to calculate from a ural to wonder whether there is a way of fundamental underlying theory. describing the physics where the interior String theory is our best attempt to make of the box makes no appearance. sense of the mysteries of quantum grav- Amazingly, such a description exists, and ity, and it perfectly exempli½es this basic is given in terms of a completely ordinary ideology. In its earliest incarnation, string quantum ½eld theory living on the walls theory computed the results of scattering of the box, made from particles very much

processes and was thought of as a gener- like the quarks and gluons of the strong Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 alization of quantum ½eld theory, with interactions. When the interactions be- point-like particles replaced by extended tween the “gluons” are made very strong, loops of string. This idea miraculously the physics is completely equivalent to passed several physical and mathematical that of string theory living on the inside of consistency checks and spawned a huge the box. In a speci½c sense, gravity, strings, amount of theoretical activity. The 1990s and an extra direction of space emerge brought a steady stream of surprises re- from the strong interactions of a perfectly vealing that string theory is not in fact a ordinary quantum ½eld theory in one low- theory of strings, but contains both point- er dimension, much like an apparently like particles as well as higher-dimensional three-dimensional image can be encoded objects as important ingredients. in a two-dimensional hologram. By the late 1990s, these developments led At ½rst sight, this holographic equiva- to an amazing realization, widely consid- lence seems impossible. If we had a ball ered to be the most important theoretical in the middle of the box, how could its advance in the ½eld in the past two de- position in the interior be encoded only cades. Early work in string theory focused on the walls? The presence of the ball in on understanding scattering processes in the interior is represented as some lump flat space-time, where time marches uni- of energy in the description on the walls; formly from the in½nite past to the in½- as the ball moves around the interior, this nite future and where space is not curved. lump correspondingly shrinks and grows But it is also possible to consider a differ- in size. What about the force of gravity ent kind of on very large scales, between two balls in the interior? The two known as anti-de Sitter space. Here, time corresponding lumps of energy modify still marches uniformly from the in½nite the virtual cloud of gluons surrounding past to the in½nite future, but space is them, which in turn induces a net attrac- curved. While the distance from a point tion between the lumps, precisely repro- on the interior to the boundary of space ducing the correct gravitational force. In is in½nite, due to the curvature, a light every physical sense, gravity and the extra beam takes a ½nite amount of time to direction of space making up the inside make it to the boundary. Thus, this geom- of the box do indeed emerge “holograph- etry can be usefully thought of as the ically,” from the dynamics of the theory inside of a box. that lives fundamentally on the walls. This There is a rich set of observables that correspondence gives us our ½rst concrete we can talk about in this geometry: start- clue as to how space-time may emerge ing on the walls, we can throw particles from more primitive building blocks.

58 Dædalus, the Journal ofthe American Academy of Arts & Sciences For the past hundred years, physics has universe is expanding. Looking back in Nima been telling us that there are fewer and time, we eventually encounter Planckian Arkani- Hamed fewer observables we can talk about mean- space-time curvatures near the “,” ingfully. The transition from classical to where all our descriptions of physics break quantum physics was the most dramatic down along with the notion of time itself. in this regard: the in½nite number of ob- An equally profound set of questions is servables in a deterministic universe was associated with understanding the uni- reduced to merely computing probabili- verse at late times. Perhaps the most im- ties. But this loss came with a silver lining: portant experimental ½nding in funda- if there are fewer fundamental observables, mental physics in the past twenty years seemingly disparate phenomena must be has been the discovery that the universe’s

more closely related and uni½ed than they expansion rate is accelerating and that Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 appear to be. In this case, the loss of deter- the universe is growing exponentially, dou- minism was directly responsible for un- bling in size every ten billion years or so. derstanding waves and particles in a uni- Due to this exponential growth, light from ½ed way. Adding gravity to the mix fur- regions of space more than ten billion ther eliminates all local observables and light years away will never make it to us: pushes the meaningful questions to the the ½nite part of the universe we now see boundary of space-time, but this is also is all we will ever have access to. This sim- what allows gravity and quantum ½eld ple observation has huge implications. As theory to be holographically equivalent to discussed above, precise observables re- each other. It is gratifying to see that all the quire a separation of the world into a) an major themes of theoretical physics over in½nitely large measuring apparatus and the past four decades, in quantum ½eld b) the system being studied. In our accel- theory and string theory, have been ex- erating universe, with access to only a ½nite ploring different aspects of a single under- (though enormous) amount of material, lying structure. But can this theoretical it is impossible to make an in½nitely large discovery be applied to understanding apparatus. Thus, we appear to have no pre- in the real world? The cise observables to talk about. So what sort box in which the gravitational theory lives of fundamental theory should we be look- can be arbitrarily large; indeed, if we did ing for to describe this situation? This is not know about cosmology, we might eas- perhaps the deepest conceptual problem ily imagine that our universe is a box of we face in physics today. Any progress on this sort, with a size of about ten billion this question must involve some essen- light years. Any questions about gravity tially new insight into the nature of time. and quantum mechanics on shorter scales, from the size of galaxies down to the Planck Having scaled these dizzyingly abstract length, can be asked equally well in this heights, let us come back down to Earth toy box as in our own universe. and ask another set of far simpler seeming But a number of conceptual challenges questions. One of the most obvious and must be overcome to describe the universe important properties of the universe is that we actually live in, and most of them have it is enormous compared to the tiny dis- to do with a deeper understanding of time. tance scales of fundamental physics, from Indeed, the major difference between our atoms and nuclei all the way down to the universe and the “gravity in a box” toy Planck length. This big universe is also model we have understood so well is that ½lled with interesting objects that are much we do not live in a static universe. Our larger than atoms. Why is there a macro-

141 (3) Summer 2012 59 The Future scopic universe when the basic constit- conclusion that the universe should be of Funda- uents of matter and all the fundamental crumpled up near 10-33 cm, or should be mental Physics distance scales are microscopic? expanding at an explosive rate, doubling This question does not at ½rst seem par- in size every 10-43 seconds. Obviously, this ticularly profound: things are big because looks nothing like the universe we live in. they are composed of a huge number of As already mentioned, the expansion rate atoms. But this is not the whole story. In of our universe is in fact accelerating, but fact, things are big as a direct consequence the universe is doubling in size every ten of the extreme weakness of gravity rela- billion years or so. The simplest explana- tive to other forces in nature. Why is the tion for this acceleration is a small pos- Earth big? Its size is determined by com- itive cosmological constant, with a size

petition between an attractive gravitation- 120 orders of magnitude smaller than our Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 al pressure that is counterbalanced by Planckian estimate. This is the largest dis- atomic pressures; planets can be so big agreement between a “back of the enve- precisely because gravity is an extremely lope” estimate and in the history weak force. Stars are big for a similar rea- of physics–all the more disturbing in a son. If the Planck length were comparable subject accustomed to twelve-decimal- to the scales of atomic and , place agreements between theory and ex- gravity would be a vastly stronger force, periment. and our planets and stars would all be Before addressing more sophisticated crushed into black holes. Thus, instead of questions, our description of nature given asking why there is a macroscopic uni- by the Standard Model must deal with the verse, we could ask: why is Planck length extremely basic question of why the uni- so much smaller than all the other scales verse is big. We have found a huge contri- in physics? bution to the cosmological constant from This turns out to be a very deep ques- quantum fluctuations, but there can also tion. One might think that the scales sim- be a purely classical part of the cosmolog- ply are what they are, and can easily be ical constant, whose size just so happens arranged to be vastly different from each to delicately cancel the contributions from other. But this is not the case. Huge quan- quantum fluctuations, to an accuracy of tum fluctuations near the Planck length 120 decimal places. This is a deeply unsat- seem to make it impossible for macro- isfying explanation, and for obvious rea- scopic phenomena to be coherent on sons is referred to as unnatural ½ne-tuning larger distance scales. of the parameters of the theory. The ½ne- The most dramatic puzzle arises from the tuning needed to understand why we have energy carried by quantum fluctuations. a big universe is known as the cosmological Fluctuations in a box of Planckian size constant problem. should carry Planckian energy, leading us There is an analogous puzzle known as to expect that the vacuum will have some the , related to the ques- energy density. This vacuum energy den- tion of why atomic scales are so much sity is known as the cosmological constant, larger than the Planck length. The rela- and we have estimated that it should be tively large size of the is a conse- set by the Planck scale. Like all other forms quence of the small mass of the electron. of matter and energy, the vacuum energy As briefly reviewed above, an electron ac- curves space-time; if the cosmological con- quires its mass from bumping into the stant is Planckian, the curvatures should Higgs ½eld, with a typical interaction also be Planckian, leading to the absurd length near 10-17 cm. But the Higgs ½eld

60 Dædalus, the Journal ofthe American Academy of Arts & Sciences itself should have enormous quantum no one has discovered a way to modify its Nima fluctuations growing stronger toward the principles even slightly. However, theorists Arkani- Hamed Planck scale, and so the typical length have found an essentially unique theoret- scale of its interactions with an electron ical structure––that can ex- should be closer to 10-33 cm. This outcome tend our notion of space-time in a new way. would make electrons sixteen orders of magnitude heavier than they are observed with supersymmetry are a spe- to be. To avoid this conclusion, we have cial kind of quantum ½eld theory that can to invoke another unnatural ½ne-tuning be thought of as extending our usual four in the parameters of the theory, this time dimensions of space and time by four addi- to an accuracy of one part in 1030. tional dimensions. The novelty is that dis-

Unlike the dif½culties with the ideas of tances in these are not Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 space-time near the Planck length, these measured by ordinary numbers, but by so-called naturalness problems do not rep- quantum variables: in a sense, supersym- resent a direct breakdown of our under- metry makes space-time more intrinsically standing of the laws of nature. But the quantum-mechanical. Ordinary distances extremely delicate adjustment of param- satisfy the basic multiplication law a x b= eters needed to answer such basic ques- b x a, and are said to be commuting vari- tions seems incredibly implausible, sug- ables. However, distances in the quantum gesting that we are missing crucial new dimensions satisfy instead a x b=-bx a, physical principles to provide a more sat- with the crucial minus sign, and are said isfying explanation for why we have a to be anti-commuting. In particular, a x a= macroscopic universe. It is as though we -a x a=0. Because of this, it is impossible see a pencil standing on its tip in the mid- to take more than a single “step” into the dle of a table. While this scenario is not im- quantum dimensions. An electron can possible, if we were confronted with this move around in our ordinary four dimen- sight we would seek an explanation, look- sions, but it can also take this single step ing for some mechanism that stabilizes into the quantum dimensions. From the the pencil and prevents it from falling over. four-dimensional point of view, it will For instance, we might look to see if the appear to be another particle, the super- pencil is secretly hanging from a string partner of the electron, with the same mass attached to the ceiling. and charge but different in its magnetic The most obvious resolution to these properties. The “” part of super- ½ne-tuning problems would be to ½nd an symmetry demands that the interactions extension of the Standard Model that respect a perfect symmetry between the somehow removes large vacuum fluctua- ordinary and the quantum dimensions. tions. Because these fluctuations are an in- Supersymmetry is a deep idea that has trinsic feature of the uni½cation of quan- played a major role in theoretical physics tum mechanics and space-time, it stands for the past forty years. It is an essential to reason that any mechanism for remov- part of string theory, it has helped revolu- ing them must change one of these two tionize our understanding of quantum ½eld pillars of quantum ½eld theory in some theory, and along the way it has opened essential way; therefore, we can start by up many new connections between physics asking whether such modi½cations are and . Among its many re- even theoretically possible. Quantum me- markable properties, the one relevant to chanics is an extremely rigid theoretical our discussion is that supersymmetry elim- structure, and in the past eight decades, inates large vacuum quantum fluctuations

141 (3) Summer 2012 61 The Future in a beautiful way. The inability to take is particularly exciting that we are prob- of Funda- more than a single step into the quantum ing exactly these distances at the lhc. mental Physics dimensions means that there can be no What about the much more severe cos- wild fluctuations in the quantum dimen- mological constant problem? The cosmo- sions; and because the quantum and ordi- logical constant is so tiny that its associ- nary dimensions must be treated sym- ated length scale is around a millimeter, metrically, there can be no large fluctua- and nature is clearly not supersymmetric tions in the ordinary dimensions either. at the millimeter scale. Supersymmetry More technically, the large fluctuations does improve the ½ne-tuning problem for from the ordinary particles are perfectly the cosmological constant from one part canceled by their superpartners. in 10120 to one part in 1060, but this is

Of course, there is a catch: we haven’t small consolation. The dif½culty is not just Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 observed any of the superpartners for the with supersymmetry: we have not seen ordinary particles! It is possible, however, any sort of new physics at the millimeter that physics at short distances is super- scale, so there is no hint that the cosmo- symmetric, but that the perfect symmetry logical constant problem is solved in a between ordinary and quantum dimen- natural way. sions is hidden by the same kind of long- This enormous challenge has led some distance illusion that hides the essential theorists to imagine a different sort of ex- unity of strong, weak, and electromagnetic planation for ½ne-tuning problems, involv- interactions. This long-distance “break- ing a radical change to our picture of space- ing” of supersymmetry has the effect of time not at short distances, but at huge making the superpartners heavier than the scales larger than the size of our observ- ordinary particles we have seen, similar able universe. The idea takes some inspi- to how the W and Z particles are heavy ration from developments in string theory while the photon is massless. over the last decade. String theory is a Can broken supersymmetry still address unique mathematical structure, but it the ½ne-tuning problems? If nature be- has long been known that it has many dif- comes supersymmetric at around 10-17 cm, ferent solutions, or vacua, each of which then the large quantum fluctuation in the corresponds to a different possible long- Higgs ½eld will be removed, yielding a distance world. The basic laws of nature completely natural resolution of the hier- are the same in all vacua, but the menu of archy problem. While there are a few other particles and interaction strengths changes approaches to the hierarchy problem, from vacuum to vacuum. The new real- supersymmetry is the most compelling, ization is that the number of vacua with and there are some strong quantitative broken supersymmetry–the ones that (though circumstantial) hints that it is on might roughly resemble our world–is gar- the right track. Whether it is supersym- gantuan: a rough estimate is that 10500 metry or something else, a natural solution such vacua may exist. Furthermore, an of the hierarchy problem demands some important idea in cosmology, known as sort of new physics at around 10-17 cm. If eternal , makes it possible that all nothing new happens until, say, 10-20 cm, these vacua are actually realized some- then the quantum fluctuation of the Higgs where in space-time. Many of these vacua ½eld will be dragged to 10-20 cm. In order have positive cosmological constants and to make the actual interaction range of are undergoing exponential expansion. 10-17 cm natural, something new must Quantum mechanics enables bubbles of show up at just this scale. This is why it a new vacuum to form in this cosmology.

62 Dædalus, the Journal ofthe American Academy of Arts & Sciences The bubble containing this “daughter” thorniest questions lie at the intersection Nima vacuum grows at nearly the speed of light of quantum mechanics, gravity, and cos- Arkani- Hamed and would naively appear to consume the mology. “parent” vacuum. But this does not hap- pen: because the parent is growing expo- What might we expect to learn from nentially, it is never completely swallowed experiments in the coming decade? The up, and it continues its exponential expan- Large Hadron Collider is perhaps the most sion forever. Thus, all possible daughter important experiment today, pushing the vacua are produced, giving rise to the pic- frontiers of fundamental physics. The ac- ture of an in½nite where all vacua celerator itself is housed in a tunnel a hun- are produced, in½nitely often, somewhere dred meters underground, with a circum-

in space-time. ference of twenty-seven kilometers. The Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 In most of these vacua, the cosmologi- tunnel contains a ring, where two sets of cal constant is enormous; but these vacua protons, moving in opposite directions, are also undergo explosive accelerated expan- accelerated to a speed 0.9999999 times sion that would rip apart all structures, so the speed of light. The protons are made in these regions the universe would be to collide head-on at two points around empty. However, there are so many vacua the ring, which are surrounded by enor- that, statistically speaking, some of them mous detectors. Two teams, each consist- will have a small cosmological constant. ing of three thousand , study the It is only in those regions that the universe debris from these collisions, which give is not empty, and so it is not surprising us a direct window into the laws of nature that we should ½nd ourselves there. at distances of order 10-17 cm, an order of This picture is currently the only rea- magnitude better than we have probed sonable explanation that we have for the before. smallness of the cosmological constant, As mentioned, a proton is not a point- and it is not impossible that similar con- like particle, but is a messy 10-14 cm bag siderations may also be relevant for the containing quarks that are permanently hierarchy problem. So, is our universe just trapped inside by gluons. When two of a tiny part of a vast and mostly lethal multi- these messy bags collide at enormous verse? If this picture is correct, it would energies, they usually break up into other be a further extension of the Copernican messy collections of strongly interacting revolution. However, a number of major particles, zooming along in the initial direc- conceptual challenges must be overcome tion of the beams. These typical inter- to determine whether these ideas make actions are not our main interest in prob- coherent sense, even on purely theoreti- ing short-distance physics. Rather, we are cal grounds. Because our own universe is after the head-on collisions between the accelerating, we can never see the other quarks and gluons in one proton and the regions in the multiverse, and so it is not quarks and gluons in the other. The tell- obvious that we can talk about these re- tale sign that a head-on collision has oc- gions in a physically and mathematically curred is that particles scatter off at large meaningful way. But it is also not impos- angles relative to the initial direction of sible to make proper sense of this picture. the beams. The collision can also produce This has been an active area of research energy enough to create new heavy parti- in the last decade, although serious theo- cles and anti-particles. retical progress on these problems still Any new particles will typically be unsta- seems rather distant. Once again, the ble, decaying on a timescale of order 10-27

141 (3) Summer 2012 63 The Future seconds into ordinary particles like elec- tral particle that is so weakly interacting of Funda- trons and positrons, quarks and anti- it sails through the detectors without leav- mental Physics quarks, and so on. These decay products ing a trace. Thus, supersymmetric events will also spray off at large angles relative should have the distinctive feature of seem- to the initial direction of the beam. Thus, ing to have “missing” energy and momen- studying all the debris from the high-ener- tum. No evidence for superpartners has gy collisions that come off at large angles yet emerged in the data, and the searches is, in general, the best probe we have for are beginning to encroach on the territory studying short-distance physics. Having where superpartners must show up, if the this rough means to discriminate “typical” supersymmetry indeed naturally solves and “interesting” events is crucial because the hierarchy problem. lhc

the interesting events are exceedingly rare After running through 2012, the Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 relative to the typical ones. There are about will stop and restart operations in 2014– a billion typical collisions per second, 2015 with twice its current energy. What whereas the timescale for producing, say, might we know by 2020? The discovery supersymmetric particles is expected to of supersymmetry would represent the be in the range of a few per minute to a ½rst extension of our notion of space- few per hour. The debris from these colli- time since Einstein and would con½rm one sions are collected by the huge detectors of the most important theoretical ideas and studied in great detail to look for the of the past forty years. We would also ½nd proverbial needle in the haystack. a completely satisfactory understanding The ½rst order of business at the lhc is of the question, why is gravity weak? On the search for the Higgs particle. As noted, the other hand, if neither supersymmetry analysis of the 2012 data should either de- nor any other sort of natural solution to ½nitively con½rm or de½nitively exclude the hierarchy problem appears in the data, its existence. (Most physicists expect the the situation will be much more confusing. former, especially following the hint We will have solid experimental evidence reported in December 2011.) Assuming for ½ne-tuning in the parameters that de- that the existence of the Higgs particle is termine , some- con½rmed, an accurate measurement of thing we have never seen in such dramatic the rate at which it is produced, and the fashion. This would strongly resonate with way it interacts with other particles, will the apparently enormous ½ne-tuning prob- shed light on whether it behaves as ex- lems associated with the cosmological con- pected in the Standard Model, or whether stant, and would give theorists a strong it has modi½ed properties that would in- incentive to take the ideas of the multi- dicate new physics. verse more seriously. The search for supersymmetry, or some It should be clear that we have arrived other natural mechanism that would solve at a bifurcatory moment in the history of the hierarchy problem, is another central fundamental physics, a moment that has goal of the lhc program. The collision enormous implications for the future of between quarks can have suf½ciently high the subject. With many theoretical spec- energy to pop the quarks into quantum ulations pointing in radically different dimensions and produce squarks, which directions, it is now up to experiment to rapidly decay to ordinary particles and render its verdict! other superpartners. In the simplest ver- sions of the theory, the lightest of all the The twentieth century was dominated by superpartners is a stable, electrically neu- the ideas of relativity and quantum me-

64 Dædalus, the Journal ofthe American Academy of Arts & Sciences chanics, and their synthesis is quantum the Galilean notion of relativity had to be Nima ½eld theory. As I have discussed, there are deformed to one that was compatible with Arkani- Hamed strong reasons to think that some essen- a maximal speed for signal propagation tially new ideas are needed in the twenty- and thus with locality. ½rst century. The lhc is poised to shed The loss of determinism in passing from signi½cant light on the question of why a classical to quantum mechanics was a macroscopic universe exists, but the ques- much more radical change in our picture tions having to do with the deeper origin of the world, and yet even this transition of space-time seem tied to the Planck was presaged in classical physics. New- scale, offering little hope for direct clues ton’s laws are manifestly deterministic; from experiment in the near future. Even given the initial position and velocity of a

so, the requirements of physical and math- particle, together with all the forces act- Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 ematical consistency have provided a ing on it, the laws of tell us where strong guide to the theoretical investiga- the particle goes in the next instant of time. tion of these questions. Indeed, the spec- However, in the century after Newton, tacular progress in string theory over the physicists and mathematicians discov- last four decades, which has time and again ered a reformulation of Newton’s laws that surprised us with unanticipated connec- led to exactly the same equations, but from tions between disparate parts of physics a completely different philosophical start- and mathematics, has been driven in this ing point. Of all the possible a way. Today, however, we confront even particle can take from A to B, it chooses deeper mysteries, such as coming to grips the one that minimizes the average value with emergent time and the application of difference between the kinetic and po- of quantum mechanics to the entire uni- tential energies along the path, a quantity verse. These challenges call for a bigger known as the action of the path. This law shift in perspective. Is there any hope for does not look deterministic: the particle taking such large steps without direct input seems to sniff out all possible paths it could from experiment? take from A to B and then chooses the one We can take some inspiration by look- that minimizes the action. But it turns out ing at the path that led from classical that the paths that minimize the action are physics to relativity and quantum mechan- precisely the ones that satisfy Newton’s ics. Some of the crucial clues to future laws. developments were lying in plain sight, Why should it be possible to talk about in the structure of existing theories. Ein- Newton’s laws in such a different way, stein’s motivations for developing both which seems to hide their most essential special and were rooted feature of deterministic evolution in time? in “obvious” properties of classical phys- We now know the deep answer to this ics. Newton’s laws already had a notion question is that the world is quantum- of Galilean relativity. However, Galilean mechanical. As pointed relativity allowed for arbitrarily large sig- out in the mid-1940s, a quantum-mechan- nal velocities and thus action at a distance. ical particle takes all possible paths from This was in conflict with Maxwell’s laws A to B; in the , the domi- of electromagnetism, in which the inter- nant contributions to the probability are actions involving electromagnetic ½elds peaked on the trajectories that minimize were local. Einstein resolved this purely the action, which are, secondarily, the ones theoretical conflict between the two pil- that satisfy Newton’s laws. Since quantum lars of classical physics by realizing that mechanics is not deterministic, the clas-

141 (3) Summer 2012 65 The Future sical limit of the theory could not land on about quantum ½eld theories, in which of Funda- Newton’s laws, but instead lands on a dif- space-time locality is not the star of the mental Physics ferent formulation of classical physics in show and these remarkable hidden struc- which determinism is not manifest but tures are made manifest. Finding this re- rather is a secondary, derived notion. formulation might be analogous to dis- If there are any clues hiding in plain covering the least-action formulation of sight today, they are lurking in the many classical physics; by removing space- astonishing properties of quantum ½eld time from its primary place in our de- theory and string theory that have been scription of standard physics, we may be uncovered over the past two decades. The in a better position to make the leap to founders of quantum ½eld theory could the next theory, where space-time ½nally

never have imagined that it might de- ceases to exist. Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 scribe a theory of gravity in a higher- dimensional curved space, and yet it does. We have learned that theories that seem completely different from the classical perspective are secretly identical at the quantum-mechanical level. Many of these developments have uncovered deep con- nections between physics and modern mathematics. Even “bread and butter” calculations in ½eld theory, needed to understand the strong interaction pro- cesses at the lhc, have revealed major sur- prises. Textbook calculations for the rates of these processes quickly lead to hun- dreds of pages of algebra, yet in recent years we have understood that the ½nal expressions can ½t on a single line. These simpli½cations are associated with a new set of completely hidden en- joyed by ordinary quantum ½eld theories. They have been sitting under our noses undetected for sixty years, and now they are exposing connections to yet another set of new structures in mathematics. Thus, while we may not have experi- mental data to tell us about physics near the Planck scale, we do have an ocean of “theoretical data” in the wonderful math- ematical structures hidden in quantum ½eld theory and string theory. These struc- tures beg for a deeper explanation. The standard formulation of ½eld theory hides these amazing features as a direct conse- quence of its deference to space-time local- ity. There must be a new way of thinking

66 Dædalus, the Journal ofthe American Academy of Arts & Sciences