9caKJg8L

1The Future of Fundamental Physics
2Nima Arkani-Hamed
3© 2012 by the American Academy of Arts & Sciences
4NIMA ARKANI-HAMED, a Fellow
5of the American Academy since
62009, is a Professor in the School
7of Natural Sciences at the Institute
8for Advanced Study. His interests
9range from quantum ½eld theory
10and string theory to cosmology and
11collider physics. He has published
12his work in the Journal of High Energy Physics, the Journal of Cosmology
13and Astroparticle Physics, and Nuclear Physics, among other places.
14Ever since Newton realized that the same force of
15gravity pulling down on an apple is also responsible
16for keeping the moon orbiting the Earth, fundamental physics has been driven by the program of
17uni½cation: the realization that seemingly disparate
18phenomena are in fact different aspects of the same
19underlying cause. By the mid-1800s, electricity and
20magnetism were seen as different aspects of electromagnetism, and a seemingly unrelated phenomenon–light–was understood to be the undulation
21of electric and magnetic ½elds.
22Relativity and quantum mechanics pushed the
23trend toward uni½cation into territory far removed
24from ordinary human experience. Einstein taught
25us that space and time are different aspects of a single entity: space-time. Energy and momentum are
26united analogously, leading to the famous equivalence between mass and energy, E = mc2, as an immediate consequence. Einstein further realized
27that space-time is not a static stage on which physics unfolds, but a dynamic entity that can curve and
28bend. Gravity is understood as a manifestation of
2953
30Abstract: Fundamental physics began the twentieth century with the twin revolutions of relativity
31and quantum mechanics, and much of the second half of the century was devoted to the construction of a theoretical structure unifying these radical ideas. But this foundation has also led us
32to a number of paradoxes in our understanding of nature. Attempts to make sense of quantum
33mechanics and gravity at the smallest distance scales lead inexorably to the conclusion that spacetime is an approximate notion that must emerge from more primitive building blocks. Furthermore, violent short-distance quantum fluctuations in the vacuum seem to make the existence of a
34macroscopic world wildly implausible, and yet we live comfortably in a huge universe. What, if
35anything, tames these fluctuations? Why is there a macroscopic universe? These are two of the
36central theoretical challenges of fundamental physics in the twenty-½rst century. In this essay, I
37describe the circle of ideas surrounding these questions, as well as some of the theoretical and
38experimental fronts on which they are being attacked.
39space-time curvature. This new picture
40of space-time made it possible to conceive
41of ideas that were impossible to articulate
42in the Newtonian picture of the world.
43Consider the most important fact about
44cosmology: we live in an expanding universe. The distance between two galaxies
45grows with time. But the galaxies are not
46rushing apart from each other into some
47preexisting space, as though blown out of
48an explosion from some common center.
49Rather, more and more space is being generated between the galaxies all the time,
50so from the vantage point of any one galaxy, the others appear to be rushing away.
51This picture, impossible to imagine in
52Newton’s universe, is an inevitable consequence of Einstein’s theory.
53Quantum mechanics represented a more
54radical departure from classical physics,
55involving a completely new conceptual
56framework, both physically and mathematically. We learned that nature is not
57deterministic, and only probabilities can
58be predicted. One consequence is the famous uncertainty principle, by which we
59cannot simultaneously know the position
60and velocity of a particle to perfect accuracy. Quantum mechanics also allowed
61previously irreconcilable phenomena to
62be understood in a uni½ed way: particles
63and waves came to be seen as limiting aspects of the underlying description where
64there are no waves at all, only quantummechanical particles.
65The laws of relativity and quantum
66mechanics are the pillars of our current
67understanding of nature. However, describing physics in a way that is compatible with both of these principles turns
68out to be extremely challenging; indeed,
69it is possible only with an extremely constrained theoretical structure, known as
70quantum ½eld theory. A quantum ½eld theory is characterized by a menu of particles
71that interact with each other in various
72ways. The nature of the interactions is
73almost completely dictated by the rules
74of quantum mechanics, together with the
75requirement that the interactions take
76place at points in space-time, in compliance with the laws of special relativity. The
77latter requirement is known as the principle of locality.
78One of the startling general predictions
79of quantum ½eld theory is the existence of
80anti-particles such as the positron, which
81has the same properties as the electron but
82the opposite electric charge. This prediction has another striking consequence:
83namely, that even the vacuum has structure and dynamics.
84Suppose we attempt to check that some
85small region of space-time is empty. Because of the uncertainty principle, we need
86higher energies to probe short distances.
87Eventually there is enough energy to make
88an electron and a positron, without violating either the conservation of energy
89or the conservation of charge. Instead of
90seeing nothing, probing the vacuum at
91small distances yields particle/anti-particle
92pairs. It is useful to think of the vacuum
93as ½lled with quantum fluctuations, with
94“virtual” particles and anti-particles popping in and out of existence on faster and
95faster timescales at shorter and shorter
96distances.
97These quantum fluctuations give rise to
98measurable physical effects. For instance,
99the cloud of virtual electrons and positrons surrounding an electron is slightly
100perturbed by the electron’s electric ½eld.
101Any physical measurement of the electron’s charge, then, will vary just slightly
102with distance, growing slowly closer in to
103the electron as more of the virtual cloud
104is pierced. These virtual effects can be calculated very precisely; in some circumstances, theoretical predictions and experimental observations can be compared to
105an astonishing level of precision. The virtual corrections to the magnetic proper54
106The Future
107of Fundamental
108Physics
109Dædalus, the Journal of the American Academy of Arts & Sciences
110ties of the electron, for example, have been
111theoretically computed to twelve decimal
112places, and they agree with experiment to
113that level of precision.
114The second-half of the twentieth century saw a flurry of activity, on both experimental and theoretical fronts. These
115developments culminated in the 1970s
116with the construction of the Standard
117Model of particle physics, a speci½c quantum ½eld theory that describes all known
118elementary particles and their interactions
119down to the smallest distances we have
120probed so far. There are four basic interactions: gravity and electromagnetism,
121which were familiar even to the ancients,
122as well as the weak and strong interactions
123that reveal themselves only on nuclear
124scales. Atomic nuclei consist of neutrons
125and protons. An isolated neutron is unstable, living for about ½fteen minutes before disintegrating into a proton, electron,
126and an anti-neutrino. (This process is also
127responsible for radioactivity.) Fifteen minutes is enormously long compared to the
128typical timescales of atoms and nuclei, so
129the interaction responsible for triggering
130this decay must be very feeble–hence,
131weak interaction. The earliest incarnation
132of the strong interaction was noticed in the
133attraction keeping protons inside nuclei,
134counterbalancing their huge electrical repulsion.
135Some familiar particles, such as electrons and photons, remain as elementary
136point-like entities in the Standard Model.
137Others, like the proton, are understood to
138be bound states, around 10-14 cm in diameter made of quarks, which are permanently trapped inside the proton through
139their interaction with gluons.
140Strong, weak, and electromagnetic interactions seem completely different from
141each other at long distances, but we now
142know that these differences are a longdistance illusion. At short scales, these interactions are described in essentially the
143same quantum-½eld-theoretic language.
144Electromagnetism is associated with interactions between electrons and photons of
145a speci½c sort. Strong interactions arise
146from essentially identical interactions between quarks and gluons, while weak interactions connect particles like the electron
147and the neutrino in the same way, with
148massive cousins of the photon known as
149the W and Z particles.
150Differences appear at long distances for
151subtle reasons. The electromagnetic interaction was the ½rst to be detected and understood because the photon is massless
152and the interaction is long-ranged. The W
153and Z particles are massive, thus mediating an interaction with a short range of
154about 10-17 cm. The difference with quarks
155and gluons is more subtle still: the virtual
156effects of the cloud of gluons surrounding a quark make the “strong charge” of
157quarks slowly grow stronger at longer distances. At a distance of roughly 10-14 cm,
158the interaction is so strong as to permanently con½ne quarks inside protons and
159neutrons.
160But from a fundamental short-distance
161perspective, these are details: the character
162of the laws is essentially identical. This
163fact illustrates the central reason why we
164probe short distances in fundamental
165physics. It is not so much because we care
166about the “building blocks of matter” and
167the associated set of particles we may discover, but because we have learned that
168the essential unity, simplicity, and beauty
169of the underlying laws manifest most
170clearly at short distances.
171The Standard Model is one of the triumphs of physics in the twentieth century.
172It gives us a simple and quantitatively accurate description of everything we know
173about elementary particles and their interactions. Only one element of the theory has
174yet to be de½nitely con½rmed by experiment. In the fundamental short-distance
175theory, where all the interactions are treat55
176Nima
177ArkaniHamed
178141 (3) Summer 2012
179ed on a symmetrical footing, the particles
180are massless. The mass of particles, such
181as electrons or the Wand Z particles, arises
182as a dynamic long-distance effect, known
183as the Higgs mechanism because of the
184particles’ interactions with the so-called
185Higgs ½eld. The typical length scale associated with these interactions is around
18610-17 cm, which is, not coincidentally, also
187the range of weak interactions. As I discuss
188at greater length below, it is also fortuitously the distance scale we are now probing with the Large Hadron Collider (lhc),
189the particle accelerator located at the cern
190laboratory just outside Geneva, Switzerland. Collisions at the lhc should put ripples in the Higgs ½eld that manifest as the
191Higgs particle with very de½nite properties and experimental signatures. Indeed,
192last December, the lhc experiments reported preliminary evidence for events
193consistent with the production of the
194Higgs particle, with its expected properties. Analysis of the 2012 data should
195either yield a de½nitive discovery of the
196Higgs particle or de½nitively exclude the
197simplest realization of the Higgs mechanism within the Standard Model.
198The success of the Standard Model gives
199us a strong indication that we are headed
200in the right direction in our understanding of fundamental physics. Yet profound
201mysteries remain, associated with questions that either lie outside the scope of the
202Standard Model or are addressed by it, but
203in a seemingly absurd way. Two of these
204questions stand out for both their simplicity and urgency, and will drive the development of fundamental physics in the
205twenty-½rst century.
206The principle of locality–the notion that
207interactions take place at points in spacetime–is one of the two pillars of quantum ½eld theory. It is therefore unsettling
208to realize that, due to the effects of both
209gravity and quantum mechanics, spacetime is necessarily an approximate notion
210that must emerge from more primitive
211building blocks.
212Because of the uncertainty principle, we
213have to use high energies to probe short
214distances. In a world without gravity, we
215could resolve arbitrarily small distances in
216this way, but gravity eventually and dramatically changes the picture. At miniscule distances, so much energy has to be
217concentrated into such a tiny region of
218space that the region itself collapses into
219a black hole, making it impossible to extract any information from the experiment.
220This occurs when we attempt to probe
221distances around 10-33 cm, the so-called
222Planck length.
223The Planck length is a ridiculously tiny
224distance scale–sixteen orders of magnitude smaller than the tiniest distances we
225are probing today at the lhc. Its tininess
226is a direct reflection of the extreme weakness of gravity compared to other forces
227of nature. The gravitational attraction between a pair of electrons is forty-two orders
228of magnitude smaller than their electrical
229repulsion. Classically, both the gravitational and electric forces vary with distance
230following an inverse-square law; however,
231at a distance of around 10-11 cm, this gets
232corrected in an important way: again because of the uncertainty principle, simply
233holding two electrons at shorter distances
234requires a huge amount of energy. The
235force of gravity increases with increasing
236mass, or with equivalently increasing energy, so the attraction between electrons
237begins to increase relative to the electrical repulsion. At around 10-31 cm, gravity
238surpasses the electric force, and at 10-33
239cm, it dominates all interactions.
240Thus, the combination of gravity and
241quantum mechanics makes it impossible
242to operationally probe Planckian distances. Every time we have encountered
243ideas in physics that cannot even in principle be observed, we have come to see such
24456
245The Future
246of Fundamental
247Physics
248Dædalus, the Journal of the American Academy of Arts & Sciences
249ideas as approximate notions. However,
250this instance is particularly disturbing because the notion that emerges as approximate is that of space-time itself.
251The description of the situation seems
252to relegate all the mysteries to tiny distances, and may suggest some sort of granular structure to space-time near the
253Planck scale. Much as the smooth surface
254of a table is resolved into discrete units
255made of molecules and atoms, one might
256imagine that “atoms of space-time” will
257replace space-time near the Planck length.
258This naive idea is very likely wrong. Any
259sort of granular structure to space-time
260picks a preferred frame of reference, where
261the size of the granularity is “small,” in
262sharp conflict with the laws of relativity.
263But there is a deeper reason to suspect
264that something much more interesting and
265subtle than “atoms of space-time” is at
266play. The problems with space-time are not
267only localized to small distances; in a precise sense, “inside” regions of space-time
268cannot appear in any fundamental description of physics at all.
269The slogan is that due to quantum mechanics and gravity, there are no “local
270observables.” Indeed, before worrying
271about what a correct theory combining
272quantum mechanics and gravity ought to
273look like, it is worth thinking about what
274perfectly precise measurements can ever
275be made by experiments. These (in principle) exact observables provide a target
276for what the theory should predict.
277Imagine trying to perform any sort of
278local measurement, by which I mean an
279experiment that can be done in a ½nitesized room. To extract a perfectly precise
280measurement, we need (among other
281things) to use an in½nitely large apparatus in order to avoid inaccuracies arising
282from the quantum fluctuations of the apparatus. If the apparatus has a large but
283½nite number of components, on a huge
284but ½nite timescale, it suffers its own quantum fluctuations, and therefore cannot
285record the results of the experiment with
286perfect accuracy. Without gravity, nothing would stop us from conducting the
287experiment with an in½nitely big apparatus to achieve perfect accuracy, but gravity obstructs this. As the apparatus gets
288bigger, it inevitably also gets heavier. If
289we are making a local measurement in a
290½nite-sized room, at some large but ½nite
291size it becomes so heavy that it collapses
292the entire room into a black hole.
293This means that there is no way, not
294even in principle, to make perfectly accurate local measurements, and thus local observables cannot have a precise meaning.
295There is an irreducible error associated
296with any local measurement that is made
297in a ½nite room. While this error is signi½-
298cant close to the Planck scale, it is negligible in ordinary circumstances. But this
299does not diminish the importance of this
300observation. The fact that quantum mechanics makes it impossible to determine
301precisely the position and velocity of a
302baseball is also irrelevant to a baseball
303player. However, it is of fundamental importance to physics that we cannot speak
304precisely of position and momentum, but
305only position ormomentum. Similarly, the
306fact that gravity makes it impossible to
307have precise local observables has the dramatic consequence that the “inside” of
308any region of space-time does not have a
309sharp meaning, and is likely an approximate notion that cannot appear in a deeper
310underlying theory.
311If we cannot speak precisely of local observables, what observables can we talk
312about? Instead of performing observations inside some region of space-time,
313we can push our detectors out to in½nite
314distances, at the boundary of space-time,
315where we can make them in½nitely big.
316We can then throw particles into the interior, where they interact and scatter with
31757
318Nima
319ArkaniHamed
320141 (3) Summer 2012
321each other in some way and emerge back
322out to in½nity where they are measured.
323The results of these scattering experiments
324can be the perfectly precise observables
325that one might hope to calculate from a
326fundamental underlying theory.
327String theory is our best attempt to make
328sense of the mysteries of quantum gravity, and it perfectly exempli½es this basic
329ideology. In its earliest incarnation, string
330theory computed the results of scattering
331processes and was thought of as a generalization of quantum ½eld theory, with
332point-like particles replaced by extended
333loops of string. This idea miraculously
334passed several physical and mathematical
335consistency checks and spawned a huge
336amount of theoretical activity. The 1990s
337brought a steady stream of surprises revealing that string theory is not in fact a
338theory of strings, but contains both pointlike particles as well as higher-dimensional
339objects as important ingredients.
340By the late 1990s, these developments led
341to an amazing realization, widely considered to be the most important theoretical
342advance in the ½eld in the past two decades. Early work in string theory focused
343on understanding scattering processes in
344flat space-time, where time marches uniformly from the in½nite past to the in½-
345nite future and where space is not curved.
346But it is also possible to consider a different kind of geometry on very large scales,
347known as anti-de Sitter space. Here, time
348still marches uniformly from the in½nite
349past to the in½nite future, but space is
350curved. While the distance from a point
351on the interior to the boundary of space
352is in½nite, due to the curvature, a light
353beam takes a ½nite amount of time to
354make it to the boundary. Thus, this geometry can be usefully thought of as the
355inside of a box.
356There is a rich set of observables that
357we can talk about in this geometry: starting on the walls, we can throw particles
358into the interior of the box and watch them
359come back out to the walls at some ½nite
360time in the future. Because these experiments start and end on the walls, it is natural to wonder whether there is a way of
361describing the physics where the interior
362of the box makes no appearance.
363Amazingly, such a description exists, and
364is given in terms of a completely ordinary
365quantum ½eld theory living on the walls
366of the box, made from particles very much
367like the quarks and gluons of the strong
368interactions. When the interactions between the “gluons” are made very strong,
369the physics is completely equivalent to
370that of string theory living on the inside of
371the box. In a speci½c sense, gravity, strings,
372and an extra direction of space emerge
373from the strong interactions of a perfectly
374ordinary quantum ½eld theory in one lower dimension, much like an apparently
375three-dimensional image can be encoded
376in a two-dimensional hologram.
377At ½rst sight, this holographic equivalence seems impossible. If we had a ball
378in the middle of the box, how could its
379position in the interior be encoded only
380on the walls? The presence of the ball in
381the interior is represented as some lump
382of energy in the description on the walls;
383as the ball moves around the interior, this
384lump correspondingly shrinks and grows
385in size. What about the force of gravity
386between two balls in the interior? The two
387corresponding lumps of energy modify
388the virtual cloud of gluons surrounding
389them, which in turn induces a net attraction between the lumps, precisely reproducing the correct gravitational force. In
390every physical sense, gravity and the extra
391direction of space making up the inside
392of the box do indeed emerge “holographically,” from the dynamics of the theory
393that lives fundamentally on the walls. This
394correspondence gives us our ½rst concrete
395clue as to how space-time may emerge
396from more primitive building blocks.
39758
398The Future
399of Fundamental
400Physics
401Dædalus, the Journal of the American Academy of Arts & Sciences
402For the past hundred years, physics has
403been telling us that there are fewer and
404fewer observables we can talk about meaningfully. The transition from classical to
405quantum physics was the most dramatic
406in this regard: the in½nite number of observables in a deterministic universe was
407reduced to merely computing probabilities. But this loss came with a silver lining:
408if there are fewer fundamental observables,
409seemingly disparate phenomena must be
410more closely related and uni½ed than they
411appear to be. In this case, the loss of determinism was directly responsible for understanding waves and particles in a uni-
412½ed way. Adding gravity to the mix further eliminates all local observables and
413pushes the meaningful questions to the
414boundary of space-time, but this is also
415what allows gravity and quantum ½eld
416theory to be holographically equivalent to
417each other. It is gratifying to see that all the
418major themes of theoretical physics over
419the past four decades, in quantum ½eld
420theory and string theory, have been exploring different aspects of a single underlying structure. But can this theoretical
421discovery be applied to understanding
422quantum gravity in the real world? The
423box in which the gravitational theory lives
424can be arbitrarily large; indeed, if we did
425not know about cosmology, we might easily imagine that our universe is a box of
426this sort, with a size of about ten billion
427light years. Any questions about gravity
428and quantum mechanics on shorter scales,
429from the size of galaxies down to the Planck
430length, can be asked equally well in this
431toy box as in our own universe.
432But a number of conceptual challenges
433must be overcome to describe the universe
434we actually live in, and most of them have
435to do with a deeper understanding of time.
436Indeed, the major difference between our
437universe and the “gravity in a box” toy
438model we have understood so well is that
439we do not live in a static universe. Our
440universe is expanding. Looking back in
441time, we eventually encounter Planckian
442space-time curvatures near the “big bang,”
443where all our descriptions of physics break
444down along with the notion of time itself.
445An equally profound set of questions is
446associated with understanding the universe at late times. Perhaps the most important experimental ½nding in fundamental physics in the past twenty years
447has been the discovery that the universe’s
448expansion rate is accelerating and that
449the universe is growing exponentially, doubling in size every ten billion years or so.
450Due to this exponential growth, light from
451regions of space more than ten billion
452light years away will never make it to us:
453the ½nite part of the universe we now see
454is all we will ever have access to. This simple observation has huge implications. As
455discussed above, precise observables require a separation of the world into a) an
456in½nitely large measuring apparatus and
457b) the system being studied. In our accelerating universe, with access to only a ½nite
458(though enormous) amount of material,
459it is impossible to make an in½nitely large
460apparatus. Thus, we appear to have no precise observables to talk about. So what sort
461of fundamental theory should we be looking for to describe this situation? This is
462perhaps the deepest conceptual problem
463we face in physics today. Any progress on
464this question must involve some essentially new insight into the nature of time.
465Having scaled these dizzyingly abstract
466heights, let us come back down to Earth
467and ask another set of far simpler seeming
468questions. One of the most obvious and
469important properties of the universe is that
470it is enormous compared to the tiny distance scales of fundamental physics, from
471atoms and nuclei all the way down to the
472Planck length. This big universe is also
473½lled with interesting objects that are much
474larger than atoms. Why is there a macro59
475Nima
476ArkaniHamed
477141 (3) Summer 2012
478scopic universe when the basic constituents of matter and all the fundamental
479distance scales are microscopic?
480This question does not at ½rst seem particularly profound: things are big because
481they are composed of a huge number of
482atoms. But this is not the whole story. In
483fact, things are big as a direct consequence
484of the extreme weakness of gravity relative to other forces in nature. Why is the
485Earth big? Its size is determined by competition between an attractive gravitational pressure that is counterbalanced by
486atomic pressures; planets can be so big
487precisely because gravity is an extremely
488weak force. Stars are big for a similar reason. If the Planck length were comparable
489to the scales of atomic and nuclear physics,
490gravity would be a vastly stronger force,
491and our planets and stars would all be
492crushed into black holes. Thus, instead of
493asking why there is a macroscopic universe, we could ask: why is Planck length
494so much smaller than all the other scales
495in physics?
496This turns out to be a very deep question. One might think that the scales simply are what they are, and can easily be
497arranged to be vastly different from each
498other. But this is not the case. Huge quantum fluctuations near the Planck length
499seem to make it impossible for macroscopic phenomena to be coherent on
500larger distance scales.
501The most dramatic puzzle arises from the
502energy carried by quantum fluctuations.
503Fluctuations in a box of Planckian size
504should carry Planckian energy, leading us
505to expect that the vacuum will have some
506energy density. This vacuum energy density is known as the cosmological constant,
507and we have estimated that it should be
508set by the Planck scale. Like all other forms
509of matter and energy, the vacuum energy
510curves space-time; if the cosmological constant is Planckian, the curvatures should
511also be Planckian, leading to the absurd
512conclusion that the universe should be
513crumpled up near 10-33 cm, or should be
514expanding at an explosive rate, doubling
515in size every 10-43seconds. Obviously, this
516looks nothing like the universe we live in.
517As already mentioned, the expansion rate
518of our universe is in fact accelerating, but
519the universe is doubling in size every ten
520billion years or so. The simplest explanation for this acceleration is a small positive cosmological constant, with a size
521120 orders of magnitude smaller than our
522Planckian estimate. This is the largest disagreement between a “back of the envelope” estimate and reality in the history
523of physics–all the more disturbing in a
524subject accustomed to twelve-decimalplace agreements between theory and experiment.
525Before addressing more sophisticated
526questions, our description of nature given
527by the Standard Model must deal with the
528extremely basic question of why the universe is big. We have found a huge contribution to the cosmological constant from
529quantum fluctuations, but there can also
530be a purely classical part of the cosmological constant, whose size just so happens
531to delicately cancel the contributions from
532quantum fluctuations, to an accuracy of
533120 decimal places. This is a deeply unsatisfying explanation, and for obvious reasons is referred to as unnatural ½ne-tuning
534of the parameters of the theory. The ½netuning needed to understand why we have
535a big universe is known as the cosmological
536constant problem.
537There is an analogous puzzle known as
538the hierarchy problem, related to the question of why atomic scales are so much
539larger than the Planck length. The relatively large size of the atom is a consequence of the small mass of the electron.
540As briefly reviewed above, an electron acquires its mass from bumping into the
541Higgs ½eld, with a typical interaction
542length near 10-17 cm. But the Higgs ½eld
54360
544The Future
545of Fundamental
546Physics
547Dædalus, the Journal of the American Academy of Arts & Sciences
548itself should have enormous quantum
549fluctuations growing stronger toward the
550Planck scale, and so the typical length
551scale of its interactions with an electron
552should be closer to 10-33 cm. This outcome
553would make electrons sixteen orders of
554magnitude heavier than they are observed
555to be. To avoid this conclusion, we have
556to invoke another unnatural ½ne-tuning
557in the parameters of the theory, this time
558to an accuracy of one part in 1030.
559Unlike the dif½culties with the ideas of
560space-time near the Planck length, these
561so-called naturalness problems do not represent a direct breakdown of our understanding of the laws of nature. But the
562extremely delicate adjustment of parameters needed to answer such basic questions seems incredibly implausible, suggesting that we are missing crucial new
563physical principles to provide a more satisfying explanation for why we have a
564macroscopic universe. It is as though we
565see a pencil standing on its tip in the middle of a table. While this scenario is not impossible, if we were confronted with this
566sight we would seek an explanation, looking for some mechanism that stabilizes
567the pencil and prevents it from falling over.
568For instance, we might look to see if the
569pencil is secretly hanging from a string
570attached to the ceiling.
571The most obvious resolution to these
572½ne-tuning problems would be to ½nd an
573extension of the Standard Model that
574somehow removes large vacuum fluctuations. Because these fluctuations are an intrinsic feature of the uni½cation of quantum mechanics and space-time, it stands
575to reason that any mechanism for removing them must change one of these two
576pillars of quantum ½eld theory in some
577essential way; therefore, we can start by
578asking whether such modi½cations are
579even theoretically possible. Quantum mechanics is an extremely rigid theoretical
580structure, and in the past eight decades,
581no one has discovered a way to modify its
582principles even slightly. However, theorists
583have found an essentially unique theoretical structure–supersymmetry–that can extend our notion of space-time in a new way.
584Theories with supersymmetry are a special kind of quantum ½eld theory that can
585be thought of as extending our usual four
586dimensions of space and time by four additional dimensions. The novelty is that distances in these extra dimensions are not
587measured by ordinary numbers, but by
588quantum variables: in a sense, supersymmetry makes space-time more intrinsically
589quantum-mechanical. Ordinary distances
590satisfy the basic multiplication law a x b =
591b x a, and are said to be commuting variables. However, distances in the quantum
592dimensions satisfy instead a x b = -b x a,
593with the crucial minus sign, and are said
594to be anti-commuting. In particular, a x a =
595-a x a=0. Because of this, it is impossible
596to take more than a single “step” into the
597quantum dimensions. An electron can
598move around in our ordinary four dimensions, but it can also take this single step
599into the quantum dimensions. From the
600four-dimensional point of view, it will
601appear to be another particle, the superpartner of the electron, with the same mass
602and charge but different in its magnetic
603properties. The “symmetry” part of supersymmetry demands that the interactions
604respect a perfect symmetry between the
605ordinary and the quantum dimensions.
606Supersymmetry is a deep idea that has
607played a major role in theoretical physics
608for the past forty years. It is an essential
609part of string theory, it has helped revolutionize our understanding of quantum ½eld
610theory, and along the way it has opened
611up many new connections between physics
612and mathematics. Among its many remarkable properties, the one relevant to
613our discussion is that supersymmetry eliminates large vacuum quantum fluctuations
61461
615Nima
616ArkaniHamed
617141 (3) Summer 2012
618in a beautiful way. The inability to take
619more than a single step into the quantum
620dimensions means that there can be no
621wild fluctuations in the quantum dimensions; and because the quantum and ordinary dimensions must be treated symmetrically, there can be no large fluctuations in the ordinary dimensions either.
622More technically, the large fluctuations
623from the ordinary particles are perfectly
624canceled by their superpartners.
625Of course, there is a catch: we haven’t
626observed any of the superpartners for the
627ordinary particles! It is possible, however,
628that physics at short distances is supersymmetric, but that the perfect symmetry
629between ordinary and quantum dimensions is hidden by the same kind of longdistance illusion that hides the essential
630unity of strong, weak, and electromagnetic
631interactions. This long-distance “breaking” of supersymmetry has the effect of
632making the superpartners heavier than the
633ordinary particles we have seen, similar
634to how the W and Z particles are heavy
635while the photon is massless.
636Can broken supersymmetry still address
637the ½ne-tuning problems? If nature becomes supersymmetric at around 10-17 cm,
638then the large quantum fluctuation in the
639Higgs ½eld will be removed, yielding a
640completely natural resolution of the hierarchy problem. While there are a few other
641approaches to the hierarchy problem,
642supersymmetry is the most compelling,
643and there are some strong quantitative
644(though circumstantial) hints that it is on
645the right track. Whether it is supersymmetry or something else, a natural solution
646of the hierarchy problem demands some
647sort of new physics at around 10-17 cm. If
648nothing new happens until, say, 10-20 cm,
649then the quantum fluctuation of the Higgs
650½eld will be dragged to 10-20 cm. In order
651to make the actual interaction range of
65210-17 cm natural, something new must
653show up at just this scale. This is why it
654is particularly exciting that we are probing exactly these distances at the lhc.
655What about the much more severe cosmological constant problem? The cosmological constant is so tiny that its associated length scale is around a millimeter,
656and nature is clearly not supersymmetric
657at the millimeter scale. Supersymmetry
658does improve the ½ne-tuning problem for
659the cosmological constant from one part
660in 10120 to one part in 1060, but this is
661small consolation. The dif½culty is not just
662with supersymmetry: we have not seen
663any sort of new physics at the millimeter
664scale, so there is no hint that the cosmological constant problem is solved in a
665natural way.
666This enormous challenge has led some
667theorists to imagine a different sort of explanation for ½ne-tuning problems, involving a radical change to our picture of spacetime not at short distances, but at huge
668scales larger than the size of our observable universe. The idea takes some inspiration from developments in string theory
669over the last decade. String theory is a
670unique mathematical structure, but it
671has long been known that it has many different solutions, or vacua, each of which
672corresponds to a different possible longdistance world. The basic laws of nature
673are the same in all vacua, but the menu of
674particles and interaction strengths changes
675from vacuum to vacuum. The new realization is that the number of vacua with
676broken supersymmetry–the ones that
677might roughly resemble our world–is gargantuan: a rough estimate is that 10500
678such vacua may exist. Furthermore, an
679important idea in cosmology, known as
680eternal inflation, makes it possible that all
681these vacua are actually realized somewhere in space-time. Many of these vacua
682have positive cosmological constants and
683are undergoing exponential expansion.
684Quantum mechanics enables bubbles of
685a new vacuum to form in this cosmology.
68662
687The Future
688of Fundamental
689Physics
690Dædalus, the Journal of the American Academy of Arts & Sciences
691The bubble containing this “daughter”
692vacuum grows at nearly the speed of light
693and would naively appear to consume the
694“parent” vacuum. But this does not happen: because the parent is growing exponentially, it is never completely swallowed
695up, and it continues its exponential expansion forever. Thus, all possible daughter
696vacua are produced, giving rise to the picture of an in½nite multiversewhere all vacua
697are produced, in½nitely often, somewhere
698in space-time.
699In most of these vacua, the cosmological constant is enormous; but these vacua
700also undergo explosive accelerated expansion that would rip apart all structures, so
701in these regions the universe would be
702empty. However, there are so many vacua
703that, statistically speaking, some of them
704will have a small cosmological constant.
705It is only in those regions that the universe
706is not empty, and so it is not surprising
707that we should ½nd ourselves there.
708This picture is currently the only reasonable explanation that we have for the
709smallness of the cosmological constant,
710and it is not impossible that similar considerations may also be relevant for the
711hierarchy problem. So, is our universe just
712a tiny part of a vast and mostly lethal multiverse? If this picture is correct, it would
713be a further extension of the Copernican
714revolution. However, a number of major
715conceptual challenges must be overcome
716to determine whether these ideas make
717coherent sense, even on purely theoretical grounds. Because our own universe is
718accelerating, we can never see the other
719regions in the multiverse, and so it is not
720obvious that we can talk about these regions in a physically and mathematically
721meaningful way. But it is also not impossible to make proper sense of this picture.
722This has been an active area of research
723in the last decade, although serious theoretical progress on these problems still
724seems rather distant. Once again, the
725thorniest questions lie at the intersection
726of quantum mechanics, gravity, and cosmology.
727What might we expect to learn from
728experiments in the coming decade? The
729Large Hadron Collider is perhaps the most
730important experiment today, pushing the
731frontiers of fundamental physics. The accelerator itself is housed in a tunnel a hundred meters underground, with a circumference of twenty-seven kilometers. The
732tunnel contains a ring, where two sets of
733protons, moving in opposite directions, are
734accelerated to a speed 0.9999999 times
735the speed of light. The protons are made
736to collide head-on at two points around
737the ring, which are surrounded by enormous detectors. Two teams, each consisting of three thousand physicists, study the
738debris from these collisions, which give
739us a direct window into the laws of nature
740at distances of order 10-17 cm, an order of
741magnitude better than we have probed
742before.
743As mentioned, a proton is not a pointlike particle, but is a messy 10-14 cm bag
744containing quarks that are permanently
745trapped inside by gluons. When two of
746these messy bags collide at enormous
747energies, they usually break up into other
748messy collections of strongly interacting
749particles, zooming along in the initial direction of the beams. These typical interactions are not our main interest in probing short-distance physics. Rather, we are
750after the head-on collisions between the
751quarks and gluons in one proton and the
752quarks and gluons in the other. The telltale sign that a head-on collision has occurred is that particles scatter off at large
753angles relative to the initial direction of
754the beams. The collision can also produce
755energy enough to create new heavy particles and anti-particles.
756Any new particles will typically be unstable, decaying on a timescale of order 10-27
75763
758Nima
759ArkaniHamed
760141 (3) Summer 2012
761seconds into ordinary particles like electrons and positrons, quarks and antiquarks, and so on. These decay products
762will also spray off at large angles relative
763to the initial direction of the beam. Thus,
764studying all the debris from the high-energy collisions that come off at large angles
765is, in general, the best probe we have for
766studying short-distance physics. Having
767this rough means to discriminate “typical”
768and “interesting” events is crucial because
769the interesting events are exceedingly rare
770relative to the typical ones. There are about
771a billion typical collisions per second,
772whereas the timescale for producing, say,
773supersymmetric particles is expected to
774be in the range of a few per minute to a
775few per hour. The debris from these collisions are collected by the huge detectors
776and studied in great detail to look for the
777proverbial needle in the haystack.
778The ½rst order of business at the lhc is
779the search for the Higgs particle. As noted,
780analysis of the 2012 data should either de-
781½nitively con½rm or de½nitively exclude
782its existence. (Most physicists expect the
783former, especially following the solid hint
784reported in December 2011.) Assuming
785that the existence of the Higgs particle is
786con½rmed, an accurate measurement of
787the rate at which it is produced, and the
788way it interacts with other particles, will
789shed light on whether it behaves as expected in the Standard Model, or whether
790it has modi½ed properties that would indicate new physics.
791The search for supersymmetry, or some
792other natural mechanism that would solve
793the hierarchy problem, is another central
794goal of the lhc program. The collision
795between quarks can have suf½ciently high
796energy to pop the quarks into quantum
797dimensions and produce squarks, which
798rapidly decay to ordinary particles and
799other superpartners. In the simplest versions of the theory, the lightest of all the
800superpartners is a stable, electrically neutral particle that is so weakly interacting
801it sails through the detectors without leaving a trace. Thus, supersymmetric events
802should have the distinctive feature of seeming to have “missing” energy and momentum. No evidence for superpartners has
803yet emerged in the data, and the searches
804are beginning to encroach on the territory
805where superpartners must show up, if the
806supersymmetry indeed naturally solves
807the hierarchy problem.
808After running through 2012, the lhc
809will stop and restart operations in 2014–
8102015 with twice its current energy. What
811might we know by 2020? The discovery
812of supersymmetry would represent the
813½rst extension of our notion of spacetime since Einstein and would con½rm one
814of the most important theoretical ideas
815of the past forty years. We would also ½nd
816a completely satisfactory understanding
817of the question, why is gravity weak? On
818the other hand, if neither supersymmetry
819nor any other sort of natural solution to
820the hierarchy problem appears in the data,
821the situation will be much more confusing.
822We will have solid experimental evidence
823for ½ne-tuning in the parameters that determine elementary particle masses, something we have never seen in such dramatic
824fashion. This would strongly resonate with
825the apparently enormous ½ne-tuning problems associated with the cosmological constant, and would give theorists a strong
826incentive to take the ideas of the multiverse more seriously.
827It should be clear that we have arrived
828at a bifurcatory moment in the history of
829fundamental physics, a moment that has
830enormous implications for the future of
831the subject. With many theoretical speculations pointing in radically different
832directions, it is now up to experiment to
833render its verdict!
834The twentieth century was dominated by
835the ideas of relativity and quantum me64
836The Future
837of Fundamental
838Physics
839Dædalus, the Journal of the American Academy of Arts & Sciences
840chanics, and their synthesis is quantum
841½eld theory. As I have discussed, there are
842strong reasons to think that some essentially new ideas are needed in the twenty-
843½rst century. The lhc is poised to shed
844signi½cant light on the question of why a
845macroscopic universe exists, but the questions having to do with the deeper origin
846of space-time seem tied to the Planck
847scale, offering little hope for direct clues
848from experiment in the near future. Even
849so, the requirements of physical and mathematical consistency have provided a
850strong guide to the theoretical investigation of these questions. Indeed, the spectacular progress in string theory over the
851last four decades, which has time and again
852surprised us with unanticipated connections between disparate parts of physics
853and mathematics, has been driven in this
854way. Today, however, we confront even
855deeper mysteries, such as coming to grips
856with emergent time and the application
857of quantum mechanics to the entire universe. These challenges call for a bigger
858shift in perspective. Is there any hope for
859taking such large steps without direct input
860from experiment?
861We can take some inspiration by looking at the path that led from classical
862physics to relativity and quantum mechanics. Some of the crucial clues to future
863developments were lying in plain sight,
864in the structure of existing theories. Einstein’s motivations for developing both
865special and general relativity were rooted
866in “obvious” properties of classical physics. Newton’s laws already had a notion
867of Galilean relativity. However, Galilean
868relativity allowed for arbitrarily large signal velocities and thus action at a distance.
869This was in conflict with Maxwell’s laws
870of electromagnetism, in which the interactions involving electromagnetic ½elds
871were local. Einstein resolved this purely
872theoretical conflict between the two pillars of classical physics by realizing that
873the Galilean notion of relativity had to be
874deformed to one that was compatible with
875a maximal speed for signal propagation
876and thus with locality.
877The loss of determinism in passing from
878classical to quantum mechanics was a
879much more radical change in our picture
880of the world, and yet even this transition
881was presaged in classical physics. Newton’s laws are manifestly deterministic;
882given the initial position and velocity of a
883particle, together with all the forces acting on it, the laws of motion tell us where
884the particle goes in the next instant of time.
885However, in the century after Newton,
886physicists and mathematicians discovered a reformulation of Newton’s laws that
887led to exactly the same equations, but from
888a completely different philosophical starting point. Of all the possible trajectories a
889particle can take from A to B, it chooses
890the one that minimizes the average value
891of difference between the kinetic and potential energies along the path, a quantity
892known as the action of the path. This law
893does not look deterministic: the particle
894seems to sniff out all possible paths it could
895take from A to B and then chooses the one
896that minimizes the action. But it turns out
897that the paths that minimize the action are
898precisely the ones that satisfy Newton’s
899laws.
900Why should it be possible to talk about
901Newton’s laws in such a different way,
902which seems to hide their most essential
903feature of deterministic evolution in time?
904We now know the deep answer to this
905question is that the world is quantummechanical. As Richard Feynman pointed
906out in the mid-1940s, a quantum-mechanical particle takes all possible paths from
907A to B; in the classical limit, the dominant contributions to the probability are
908peaked on the trajectories that minimize
909the action, which are, secondarily, the ones
910that satisfy Newton’s laws. Since quantum
911mechanics is not deterministic, the clas65
912Nima
913ArkaniHamed
914141 (3) Summer 2012
915sical limit of the theory could not land on
916Newton’s laws, but instead lands on a different formulation of classical physics in
917which determinism is not manifest but
918rather is a secondary, derived notion.
919If there are any clues hiding in plain
920sight today, they are lurking in the many
921astonishing properties of quantum ½eld
922theory and string theory that have been
923uncovered over the past two decades. The
924founders of quantum ½eld theory could
925never have imagined that it might describe a theory of gravity in a higherdimensional curved space, and yet it does.
926We have learned that theories that seem
927completely different from the classical
928perspective are secretly identical at the
929quantum-mechanical level. Many of these
930developments have uncovered deep connections between physics and modern
931mathematics. Even “bread and butter”
932calculations in ½eld theory, needed to
933understand the strong interaction processes at the lhc, have revealed major surprises. Textbook calculations for the rates
934of these processes quickly lead to hundreds of pages of algebra, yet in recent
935years we have understood that the ½nal
936expressions can ½t on a single line. These
937simpli½cations are associated with a new
938set of completely hidden symmetries enjoyed by ordinary quantum ½eld theories.
939They have been sitting under our noses
940undetected for sixty years, and now they
941are exposing connections to yet another
942set of new structures in mathematics.
943Thus, while we may not have experimental data to tell us about physics near
944the Planck scale, we do have an ocean of
945“theoretical data” in the wonderful mathematical structures hidden in quantum
946½eld theory and string theory. These structures beg for a deeper explanation. The
947standard formulation of ½eld theory hides
948these amazing features as a direct consequence of its deference to space-time locality. There must be a new way of thinking
949about quantum ½eld theories, in which
950space-time locality is not the star of the
951show and these remarkable hidden structures are made manifest. Finding this reformulation might be analogous to discovering the least-action formulation of
952classical physics; by removing spacetime from its primary place in our description of standard physics, we may be
953in a better position to make the leap to
954the next theory, where space-time ½nally
955ceases to exist.
95666
957The Future
958of Fundamental
959Physics
960Dædalus, the Journal of the American Academy of Arts & Sciences