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THE POSSIBILITY OF STRING THEORY

THE POSSIBILITY OF STRING THEORY

by SWIN HUANG

MOHAWK FINE PAPERS INC. 465 Saratoga Street Cohoes, NY 12047465 TEL: 1-800-THE MILL TEL: 1-800-843-6455 FAX: 1-518-237-7394 www.mohawkpaper.com mohawk@mohawkpaper.com

E-LE-VEN: The possibility of string theory. Copyright Š 2010 by Mohawk Fine Paper Inc. Manifactured in America.

All rights reserved. No other part of this book may be reproduced in any other form or by any electronic or mechanical means including information storage and retrieval systems without permission of copy right holder.

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I dedicate this book to my family, who will always be the love of my life.

INTRODUCTION

FOR MOST OF US, OR PERH A PS A LL OF US, IT’S IMPOSSIBLE TO IMAGINE A WORLD CONSISTING OF MOR E T H A N T HR EE SPATIAL DIMENSIONS. WITH T HE BEST OF MOH AW K V EL LUM, S AT IN 2.0 A ND TOMOH AW K F ELT PLUS EIGH T NE W SH A DES FOR A NE W PERSPECT I V E ON VA LUE PA PERS. T HE NE W V I A PORT FOLIO IS MOR E COMPR EHENSI V E—Y ET ST IL L SIMPL E. W I T H A V ERS AT IL E PA L ET T E OF CON T EMPOR A RY COLORS, V I A COMBINES A L L T HE R IGH T FINISHES, E XCEP T IONA L PR IN T QU A LI T Y, 30% A ND 100% POSTCONSUMER (PCW ) R EC YCL ED I T EMS, DIGI TA L I-TONE I T EMS, A ND 25% COT TON W R I T ING — A L L M A NUFACT UR ED GR EEN-E CERT IFIED W INDPOW ER, “VIA” C A N F UL L F IL L Y OUR IM AGINATION OF GOING TO OTHER DIMENSIONS.

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FOR MOST OF US, OR PERHAPS ALL OF US, IT’S IMPOSSIBLE TO IMAGINE A WORLD CONSISTING OF MORE THAN THREE SPATIAL DIMENSIONS. ARE WE CORRECT WHEN WE INTUIT THAT SUCH A WORLD COULDN’T EXIST? OR IS IT THAT OUR BRAINS ARE SIMPLY INCAPABLE OF IMAGINING ADDITIONAL DIMENSIONS— DIMENSIONS THAT MAY TURN OUT TO BE AS REAL AS OTHER THINGS WE CAN’T DETECT?

FROM 2-D TO 3-D An early attempt to explain the concept of extra dimensions came in 1884 with the publication of Edwin A. Abbott’s Flatland: A Romance of Many Dimensions. This novel is a “first-person” account of a two-dimensional square who comes to appreciate a three-dimensional world. + The square describes his world as a plane populated by lines, circles, squares, triangles, and pentagons. Being two-dimensional, the inhabitants of Flatland appear as lines to one another. They discern one another’s shape both by touching and by seeing how the lines appear to change in length as the inhabitants move around one another. + One day, a sphere appears before the square. To the square, which can see only a slice of the sphere, the shape before him is that of a two-dimensional circle. The sphere has visited the square intent on making the square understand the three-dimensional world that he, the sphere, belongs to. He explains the notions of “above” and “below,” which the square confuses with “forward” and “back.” When the sphere passes through the plane of Flatland to show how he can move in three dimensions, the square sees only that the line he’d been obser ving gets shor ter and shor ter and then disappears. No matter what the sphere says or does, the square cannot comprehend a space other than the two-dimensional world that he knows. + Only after the sphere pulls the square out of his two-dimensional world and into the world of Spaceland does he f inally under stand the concept of three dimensions. From this new per spective, the square has a bird’s-eye view of Flatland and is able to see the shapes of his fellow inhabitants (including, for the f irst time, their insides). + Armed with his new understanding, the square conceives the possibility of a fourth dimension.

He even goes so far as to suggest that there may be no limit to the number of spatial dimensions. In trying to convince the sphere of this possibility, the square uses the same logic that the sphere used to argue the existence of three dimensions. The sphere, now the shortsighted one of the two, cannot comprehend this and does not accept the square’s arguments—just as most of us “spheres” today do not accept the idea of extra dimensions.

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ONLY AFTER THE SPHERE PULLS THE SQUARE OUT OF HIS TWO DIMENSIONAL WORLD AND INTO THE WORLD OF SPACELAND DOES HE FINALLY UNDERSTAND THE CONCEPT OF THREE DIMENSIONS. FROM THIS NEW PERSPECTIVE, THE SQUARE HAS A BIRD’S-EYE VIEW OF FLATLAND AND IS ABLE TO SEE THE SHAPES OF HIS FELLOW INHABITANTS.

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It’s diff icult for us to accept the idea because when we try to imagine even a single additional spatial dimension—much le s s si x or seven—we hi t a br ick w all. T her e’s no going beyond i t, not w i t h our br ains apparently. + Imagine, for instance, that you’re at the center of a hollow sphere. The distance between you and every point on the sphere’s surface is equal.

N o w, t r y m o v in g in a dir e c t ion t h a t allo w s y o u t o move aw ay fr om all point s on t he spher e’s sur face w hile m ain t ainin g t h a t e q uidi s t an c e. Yo u c an’ t d o i t . T h e r e’s n o w h e r e t o g o — n o w h e r e t h a t w e k n o w any w ay. + T he squar e in Flatland w ould have t he same trouble if he were in the middle of a circle.

H e c a n’ t b e a t t h e c e n t e r o f a c i r c l e a n d m o v e i n a dir e c t ion t h a t allo w s him t o r e m ain e q uidi s t an t t o ever y point of the circle’s circumference—unless he moves into the third dimension. Alas, we don’ t have the four-dimensionsal equivalent of A bbot t’s threedimensional sphere to show us the way to 4-D.

FROM 4-D TO OTHER DIMENSIONS In 1919, Polish mathematician T heodor Kaluza proposed that the existence of a fourth spatial dimension might allow the linking of general relativity a n d e le c t r o m ag n e t ic t h e o r y.T h e id e a,l a t e r w a s ref ined by Oskar Klein, the Swedish mathematician, was that space consisted of both extended and curled-up dimensions. The extended dimensions are the three spatial dimensions that we’re familiar with,and the curled-up dimension is found deep within the ex tended dimensions and can be thought of as a circle. Experiments later showed that Kaluza and Klein’s curled-up dimension did not unite general r elati v i t y and elec t r omagne tic t heor y as or iginall y h o p e d , b u t d e c a d e s l a t e r, s t r i n g t h e o r i s t s f o u n d t h e ide a u s e f ul, e v e n m or e, n e c e s s ar y. + The mat hematic s used in super st r ing t heor y r equir e s a t l e a s t 1 0 d i m e n s i o n s . T h a t i s, f o r t h e e q u a t i o n s t hat de scr ibe super st r ing t heor y to begin to w or k out—for the equations to connect general relativity to quantum mechanics, to explain the nature of particles, to unif y for ce s, and so on—t hey need to make use of additional dimensions. These dimensions, string theorists believe, are wrapped up in the curled-up space first described by Kaluza and Klein. + To extend the curled-up space to include these added dimensions, imagine that spheres replace the Kaluza-Klein circles. Instead of one added dimension we have two if we consider only the spheres’ surfaces and three if we take into account the space within the sphere. That’s a total of six dimensions so far. So where are the others that superstring theory requires? + It turns out that, before superstring theory existed, t wo mathematicians, Eugenio C alabi of the Univer sit y of Pennsylvania and Shing-Tung Yau of Harvard University, described six-dimensional geometrical s h ap e s t h a t s up e r s t r in g t h e or i s t s s a y f i t t h e bill f or t h e k in d o f s t r uc t ur e s their equations call for. If we replace the spheres in curled-up space with these Calabi-Yau shapes, we end up with 10 dimensions: three spatial, plus the six of the Calabi-Yau shapes, plus one of time. + If superstring theory turns out to be correct, the idea of a world consisting of 10 or more dimensions is one that we’ll need to bec ome c omfor t able w i t h. Bu t w ill t her e ever be an explanation or a visual representation of higher dimensions that will truly satisf y the human mind ? T he answer to t his que stion may for ever be no. Not unle s s some fourdimensional life-for m pulls us fr om our t hr ee-dimensional Spaceland and gi ve s us a view of the world from its perspective.

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IT TURNS OUT THAT, BEFORE SUPERSTRING THEORY EXISTED, TWO MATHEMATICIANS, EUGENIO CALABI OF THE UNIVERSITY OF PENNSYLVANIA AND SHINGTUNG YAU OF HARVARD UNIVERSITY, DESCRIBED SIXDIMENSIONAL GEOMETRICAL SHAPES THAT SUPERSTRING THEORISTS SAY FIT THE BILL FOR THE KIND OF STRUCTURES THEIR EQUATIONS CALL FOR.

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FROM 4-D TO OTHER DIMENSIONS In 1919, Polish mathematician T heodor Kaluza proposed that the existence of a fourth spatial dimension might allow the linking of general relativity a n d e le c t r o m ag n e t ic t h e o r y.T h e id e a,l a t e r w a s ref ined by Oskar Klein, the Swedish mathematician, was that space consisted of both extended and curled-up dimensions. The extended dimensions are the three spatial dimensions that we’re familiar with,and the curled-up dimension is found deep within the ex tended dimensions and can be thought of as a circle. Experiments later showed that Kaluza and Klein’s curled-up dimension did not unite general r elati v i t y and elec t r omagne tic t heor y as or iginall y h o p e d , b u t d e c a d e s l a t e r, s t r i n g t h e o r i s t s f o u n d t h e ide a u s e f ul, e v e n m or e, n e c e s s ar y. + The mat hematic s used in super st r ing t heor y r equir e s a t l e a s t 1 0 d i m e n s i o n s . T h a t i s, f o r t h e e q u a t i o n s t hat de scr ibe super st r ing t heor y to begin to w or k out—for the equations to connect general relativity to quantum mechanics, to explain the nature of particles, to unif y for ce s, and so on—t hey need to make use of additional dimensions. These dimensions, string theorists believe, are wrapped up in the curled-up space first described by Kaluza and Klein. + To extend the curled-up space to include these added dimensions, imagine that spheres replace the Kaluza-Klein circles. Instead of one added dimension we have two if we consider only the spheres’ surfaces and three if we take into account the space within the sphere. That’s a total of six dimensions so far. So where are the others that superstring theory requires? + It turns out that, before superstring theory existed, t wo mathematicians, Eugenio C alabi of the Univer sit y of Pennsylvania and Shing-Tung Yau of Harvard University, described six-dimensional geometrical s h ap e s t h a t s up e r s t r in g t h e or i s t s s a y f i t t h e bill f or t h e k in d o f s t r uc t ur e s their equations call for. If we replace the spheres in curled-up space with these Calabi-Yau shapes, we end up with 10 dimensions: three spatial, plus the six of the Calabi-Yau shapes, plus one of time. + If superstring theory turns out to be correct, the idea of a world consisting of 10 or more dimensions is one that we’ll need to bec ome c omfor t able w i t h. Bu t w ill t her e ever be an explanation or a visual representation of higher dimensions that will truly satisf y the human mind ? T he answer to t his que stion may for ever be no. Not unle s s some fourdimensional life-for m pulls us fr om our t hr ee-dimensional Spaceland and gi ve s us a view of the world from its perspective.

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IT TURNS OUT THAT, BEFORE SUPERSTRING THEORY EXISTED, TWO MATHEMATICIANS, EUGENIO CALABI OF THE UNIVERSITY OF PENNSYLVANIA AND SHINGTUNG YAU OF HARVARD UNIVERSITY, DESCRIBED SIXDIMENSIONAL GEOMETRICAL SHAPES THAT SUPERSTRING THEORISTS SAY FIT THE BILL FOR THE KIND OF STRUCTURES THEIR EQUATIONS CALL FOR.

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STRING THEORISTS ARE BETTING THAT EXTRA DIMENSIONS DO EXIST; IN FACT, THE EQUATIONS THAT DESCRIBE SUPERSTRING THEORY REQUIRE A UNIVERSE WITH NO FEWER THAN 10 DIMENSIONS. BUT EVEN PHYSICISTS WHO SPEND ALL DAY THINKING ABOUT EXTRA SPATIAL DIMENSIONS HAVE A HARD TIME DESCRIBING WHAT THEY MIGHT LOOK LIKE OR HOW WE APPARENTLY FEEBLE-MINDED HUMANS MIGHT APPROACH AN UNDERSTANDING OF THEM. THAT IS ALWAYS BEEN THE CASE, AND MAYBE ALWAYS WILL BE.

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contains a vibrating, oscillating, dancing filament that physicists have named a string.

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BASIC PROPERT Y

According to string theory, if we could examine these particles with even greater precision—a precision many orders of magnitude beyond our present technological capacity—we would find that each is not pointlike but instead consists of a tiny, onedimensional loop. Like an infinitely thin rubber band, each particle

Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These m u sic al n o t e s c o uld b e s aid t o b e exc i t a t ion m o de s o f t h a t g ui t ar s t r in g un de r tension. + In a similar manner, in st r ing t heor y, t he element ar y par ticle s we obser ve in par ticle acceler ator s c ould be t hought of as t he “music al note s” or excitation modes of elementar y strings. + In string theor y, as in guitar playing, the string must be stretched under tension in order to become excited. However, t he st r ings in st r ing t heor y ar e f loating in space time, t hey ar en’ t tied dow n to a gui t ar. None t hele s s, t hey have tension. T he st r ing tension in st r ing t heor y is denoted by t he quanti t y 1 / (2 p a’), w her e a’ is pr onounced “alpha pr ime” and is e q u al t o t h e s q u ar e o f t h e s t r in g le n g t h s c ale. + I f s t r in g t h e or y i s t o b e a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravit y, called the Planck length, which is about 1 0 -3 3 c e n t im e t e r s, or a b o u t a million t h o f a billion t h o f a billion t h o f a billion t h of a centimeter. Unfortunately, this means that strings are way too small to see by current or expected particle physics technology and so string theorists must dev ise mor e clever me t hods to te st t he t heor y t han just look ing for li t tle st r ings in particle experiments. + String theories are classif ied according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there m u s t b e a s p e c i a l k i n d o f s y m m e t r y c a l l e d s u p e r s y m m e t r y, w h i c h m e a n s f o r every boson (particle that transmits a force) there is a corresponding fermion (par ticle that makes up mat ter). So super symmetr y relates the par ticles that t r an s mi t f or c e s t o t h e p ar t ic le s t h a t m a ke up m a t t e r. + S up e r s y mm e t r ic p ar t ne r s t o t o c ur r e n t l y k n o w n p ar t ic le s h a v e n o t b e e n ob s e r v e d in p ar t ic le experiments, but theorists believe this is because supersymmetric particles are too massive to be detected at current accelerators. Particle accelerators could be on the verge of finding evidence for high energy supersymmetry in the nex t dec ade. Ev idence for super sy mme t r y at high ener g y w ould be c ompelling ev idence t hat st r ing t heor y w as a good mat hematic al model for Nat ur e at t he smallest distance scales.

T her e a r e t w o ba sic t y pes of st r i ng t heor ies : t hose w it h c losed st r i ng loops t h at c a n br ea k i nto open st r i ngs , s ho w n a bo v e, a nd t hose w it h c losed st r i ng loops t h at c a n’t br ea k i nto open st r i ngs ,

THE SIZE OF THE STRING

T he strings of string theor y are unimaginably small.

Average string, if it exists, is about 10-33 centimeters long. T hat's a point followed by 32 zeros and then a 1.

It's a millionth of a billionth of a billionth of a billionth of a centimeter. (Physicists stick to metric). Or think o f i t t hi s w a y : i f an a t om w e r e m agni f ie d t o t h e si z e o f t h e s o l ar s y s t e m, a s t r in g w o uld b e t h e si z e o f a t r ee. + St ar ting at an ever yday sc ale, we t r avel by powers of 100 down into the shadow y world of s t r i n g s . T h a t i s, w e b e g i n 1 0 m e t e r s a w a y f r o m a n diamond, then zoom 100 times closer to 10 centimeters away from its skin, then 100 times closer again to one millimeter from its skin, and so on, down no fewer t han 15 addi tional power s of 10 0 until we r e ach t he Planck leng t h. Since t he Planck leng t h is r oughl y 17 or de r s o f m agni t ude s m alle r t h an w h a t p h y sic i s t s can currently detect using their largest particle accelerators (in fact, to see individual strings we would need an accelerator the size of the Milky Way), we have taken a kind of visual poetic licence in imagining what the world looks like smaller than a quark. We hope you enjoy this journey into the infinitesimally itsy-bitsy.

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SUPERSYMMETRY In cur r ent pa rticle exper iments w e c a n' t y et see a n y dir ec t e v idence for the ex is tence of superpa rtners for k now n elementa ry pa rticles ( ther e is some indir ec t e v idence, how e v er).

Ther e is a good ch a nce w e could s ta rt to see super pa rtners in futur e pa rticle ex per iments.

In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners. In a theory with unbroken supersymmetry, for every type of boson there exists a corresponding type of fermion with the same m a s s an d in t e r n al q u an t um n um b e r s, an d v ic e -v e r s a. + S o f ar, t h e r e i s onl y indirect evidence for the existence of super symmetr y. Since the superpar tner s of the Standard Model par ticles have not been obser ved, super symmetr y, if it exist s, must be a br oken sy mme t r y, allow ing t he super par ticle s to be he av ier than the corresponding Standard Model particles. + If supersymmetry exists c lo s e t o t h e TeV e n e r g y s c ale, i t allo w s f or a s o lu t ion o f t h e hie r ar c h y pr oble m o f t h e S t a n d a r d M o d e l ,i . e . , t h e f a c t t h a t t h e H i g g s b o s o n m a s s i s s u b j e c t t o quantum corrections which—barring extremely fine-tuned cancellations among independent contributions—would make it so large as to undermine the internal c on si s t e n c y o f t h e t h e or y. In s up e r s y mm e t r ic t h e or ie s, on t he o t h e r h and, t h e contributions to the quantum corrections coming from Standard Model particles are naturally canceled by the contributions of the corresponding superpartners.

Other attractive features of TeV-scale supersymmetry are the fact that it allows for the high-energy unification of the weak interactions, the strong interactions and electromagnetism, and the fact that it provides a candidate for Dark Mat ter and a nat ur al mechanism for elec t r owe ak sy mme t r y br e ak ing. + A not her advantage of supersymmetry is that supersymmetric quantum f ield theory can sometimes be solved. Supersymmetry is also a feature of most versions of string theory, though it can exist in nature even if string theory is incorrect.

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C a n c el l at i o n o f t h e h i g g s b o s o n q u a d r at i c m a s s r e n o r m a l i z at i o n bet ween fer mionic top q uark loop and scalar stop sq uark tadpole fe y n man diag rams in a supersy m metr ic ex tension of the s t a n d a r d m o d el

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DUAL ALITIES IN PHYSICS NOTE THAT IN THE TYPE IIA AND TYPE IIB STRING THEORIES CLOSED STRINGS ARE ALLOWED TO MOVE EVERYWHERE THROUGHOUT THE TENDIMENSIONAL SPACETIME (CALLED THE BULK), WHILE OPEN STRINGS HAVE THEIR ENDS ATTACHED TO D-BRANES, WHICH ARE MEMBRANES OF LOWER DIMENSIONALITY (THEIR DIMEN-

B e f o r e t h e 1 9 9 0 s, s t r i n g t h e o r i s t s b e l i e v e d t h e r e wer e f i ve distinc t super st r ing t heor ie s: open t y pe I, c lo s e d t y p e I, c lo s e d t y p e II A , c lo s e d t y p e IIB, an d t h e t w o f l a v or s o f h e t e r o t ic s t r in g t h e or y (S O (3 2) a n d E 8 Ă— E 8) . T h e t h i n k i n g w a s t h a t o u t o f t h e s e f ive c andidate theories, only one was the ac tual c or r e c t t h e or y o f e v e r y t hin g, an d t h a t t h e or y w a s t he one w hose low ener g y limi t, w i t h ten space time d i m e n s i o n s c o m p a c t i f i e d d o w n t o f o u r, m a t c h e d t h e p h y s i c s o b s e r v e d i n o u r w o r l d t o d a y. I t i s n o w believed that this picture was incorrect and that t he f i ve super st r ing t heor ie s ar e c onnec ted to one another as if they are each a special case of some mor e fundament al t heor y (t hought to be M-t heor y).

T hese theories are related by transformations that are called dualities. If t wo theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theor y. T he t wo theories are then said to be dual to one another under that kind of transformation. Put differently, the t wo theories are mathematically different descriptions of the same phenomena. + These dualities link quantities that w e r e al s o t h o ugh t t o b e s e p ar a t e. L ar ge an d s m all distance scales, as well as strong and weak coupling st r eng t hs, ar e quanti tie s t hat have al w ay s mar ked ver y distinct limits of behavior of a physical system in bot h clas sic al f ield t heor y and quant um par ticle physics. But strings can obscure the difference bet ween large and small, strong and weak, and this is how these five very different theories end up being related. T-duality relates the large and small distance sc ale s be t ween st r ing t heor ie s, w her e as S -duali t y relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.

IIB 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral).

HO 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO.

HE 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8 x E8

BOSONIC 26 Only bosons, no fermions means only forces, no matter, with both open and closed strings. Major flaw: a particle with imaginary mass, called the tachyon.

I 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO.

IIA 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral).

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ONE SUCH THEORY IS THE 11-DIMENSIONAL M-THEORY, WHICH REQUIRES SPACETIME TO HAVE ELEVEN DIMENSIONS, AS OPPOSED TO THE USUAL THREE SPATIAL DIMENSIONS AND THE FOURTH DIMENSION OF TIME.

A n in t r ig uin g fe a t ur e o f s t r in g t h e or y i s t h a t i t involves the prediction of extra dimensions.The number of dimensions is not f ixed by any consistency criterion, but flat spacetime solutions do exist in the so-called “critical dimension”. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions—more precisely different value s of t he “ef fec ti ve cent r al char ge”, a c ount of degrees of freedom which reduces to dimensionality in weakly cur ved regimes—are related by dynamical transitions. + O n e s u c h t h e o r y i s t h e 1 1d i m e n s i o n a l M -t h e o r y, w h i c h r e q u i r e s s p a c e t i m e to have eleven dimensions, as opposed to t he usual t hr e e s p a t i al dim e n sion s an d t h e f o ur t h dim e n sion of time. The original string theories from the 1980s describe special cases of M-theor y where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But t he t heor y also de scr ibe s uni ver se s like our s, w i t h f o u r o b s e r v a b l e s p a c e t i m e d i m e n s i o n s, a s w e l l as uni ver se s w i t h up to 10 f lat space dimensions, and also cases where the position in some of the dimensions is not described by a real number, but by a completely different type of mathematical quantity. So the notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different cir cumst ance s. + Not hing in Ma x well’s t heor y of electromagnetism or Einstein’s theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions “by hand”, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, t hi s h app e n s b e c au s e a g auge an om al y ex i s t s f or e v e r y s e p ar a t e n um b e r o f predicted dimensions, and the gauge anomaly can be counteracted by including n on t r i v i al p o t e n t i al e n e r g y in t o e q u a t ion s t o s ol v e m o t ion. F ur t h e r m or e, t h e absence of potential energy in the “critical dimension” explains why flat spacetime solutions are possible. + This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which r epr e sent s t he photon. T his ener g y include s a c ont r ibu tion fr om t he C asimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions. + When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). The subset of X is equal to the relation of photon fluxuations in a linear dimension. Flat space string theories are 26-dimensional in the bosonic case, while super string and M-theories turn out to involve 10 or 11 dimensions for f lat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional spacetime.

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THE SURFACE AREA OF THE EVENT HORIZON OF A BLACK HOLE CAN ONLY INCREASE, NEVER DECREASE. THIS ALSO MEANS THAT ALTHOUGH TWO BLACK HOLES CAN JOIN TO MAKE A BIGGER BLACK HOLE, ONE BLACK HOLE CAN NEVER SPLIT IN TWO. THE PULL OF GRAVITY AT THE EVENT HORIZON IS CONSTANT; IT HAS THE SAME VALUE EVERYWHERE ON THE EVENT HORIZON.

WHAT’S INSIDE THE BL ACK HOLE ?

E S C A P E V E L OC I T Y ?

FUZZBALLS ?

A NOT HER DIMENSION ?

NOTHING ?

In t h e a b s t r ac t t h e or e t ic al m o de l o f bl ac k h o le s, a bl ac k h o le i s s t udie d a s i f i t w e r e t h e onl y t hin g in the Univer se. Using that approximation, the math of gener al r elativit y becomes doable, and we c an make pr edic tions abou t black hole behav ior t hat ar e u s e f ul in un de r s t andin g t h e bl ac k h o le s w e s e e. In addi t ion, w e le ar n a lo t o f t hin g s a b o u t bl ac k h o le s mathematically that we may never get a chance to w i t ne s s dir ec tl y t hr ough obser vation. + In general relativity, the paths of light can be calculated for many different distributions of matter and energy using equations call the geodesic equations.

The geodesic equations give us the paths that would be followed by fr eely-falling te st par ticle s. For example, a baseball af ter being hi t by S ammy S os a and before being caught by an eager fan would be a freely falling par ticle, travelling on a geodesic path through spacetime. + Light travels on geodesics paths through spacetime. When those geodesic pat hs cr os s t he event hor izon of a black hole, t hey n e v e r c om e b ac k o u t . In t e r e s t in gl y, in a U ni v e r s e w h e r e t h e e n e r g y d e n s i t y i s n e v e r n e g a t i v e, t h i s behav ior of light le ads mat hematic all y to t w o ver y crucial properties of black holes: 1. The surface area of the event horizon of a black hole can only increase, never decrease. T his also means that although t wo black holes can join to make a bigger black hole, one black hole c an never spli t in t w o. 2. T he pull of gr av i t y at t he event hor izon is constant; it has the same value every where on the event horizon. + Note t hat acc or ding to t he f ir st pr oper t y, i t is impos sible for black hole s to dec ay and go away, because a black hole cannot get smaller or split into smaller black holes. This is going to be changed when we add quantum mechanics to the theory.

If a black hole traps all the light that crosses the event horizon, then how can we ever hope to obser ve one? + In the abstract theoretical model of a black hole, it sits alone forever in the Univer se let ting us do math on it. In the Nature we observe, the Universe is f illed with dust and gas in addition to stars, planets and galaxies. When dust and gas fall into a black hole, they can be sucked towards the event horizon so fast that the atoms are ionized and release bright light that e s c ap e s w i t h o u t c r o s sin g t h e e v e n t h or i z on. + S o t h e w a y a s t r on om e r s and astrophysicists detect black holes in astronomical obser vations is to look f or ligh t f r om ioni z e d d u s t an d g a s b ein g s uc ke d in t o s om e t hin g s o f a s t t h a t it could only be a black hole, not a normal gravitating massive object like a star. + H o w e v e r, t h i s b r i g h t l i g h t c a n b e h a r d t o s e e, b e c a u s e m o s t b l a c k h o l e s a l s o a t t r a c t g i a n t c l o u d s o f i n t e r s t e l l a r d u s t t h a t h i d e m a n y o f t h e i r f e a t u r e s, as show n on t he pr ev ious page. T he suspec ted black hole show n in t he photo above has a warped dust cloud around it, so that the bright light from the ionized gas can be seen.

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SPA CE T IME

WHAT’S BEFORE THE BIG BANG ?

It seems fairly likely that there was a Big Bang. The obvious question that could be asked to challenge or define the boundaries between physics and metaphysics is: what came before the Big Bang? + Physicists def ine the boundaries of physics by trying to describe them theoretically and then testing that description against observation. Our observed expanding Universe is very well described by flat space, with critical density supplied mainly by dark matter and a cosmological constant, that should expand forever. + If we follow this model backwards in time to when the Univer se was ver y hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental understanding of particle physics starts to poop out after the energy scale of electroweak unif ication, and theoretical p h y sic i s t s h a v e t o r e ac h f or m o de l s o f p ar t ic le p h y sic s b e y ond t h e S t an d ar d Model, to Gr and Unif ied T heor ie s, super sy mme t r y, st r ing t heor y and quant um cosmology.+ If we follow this model backwards in time to when the Universe was very hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental under standing of par ticle physics star ts to poop out after the energy scale of elec t r owe ak unif ic ation, and t heor e tic al phy sicist s have to r e ach for models o f p a r t i c l e p h y s i c s b e y o n d t h e S t a n d a r d M o d e l , t o G r a n d U n i f i e d T h e o r i e s, super symmetr y, string theor y and quantum cosmology. + A big complicating fac tor in under st anding st r ing c osmolog y is under st anding st r ing t heor ie s.

St r ing t heor ie s and M t heor y appe ar to be limi ting c ase s of some bigger, mor e fundament al t heor y. Until t hat’s sor ted ou t, any t hing we t hink we k now today is potentially up for grabs.

1. CAN STRING THEORY MAKE ANY COSMOLOGICAL PREDICTIONS RELEVANT TO BIG BANG PHYSICS? 2.

WHAT HAPPENS TO THE EX TR A DIMENSIONS? 3. IS THERE INFL ATION IN STRING THEORY? 4. WHAT CAN STRING THEORY TELL US ABOUT QUANTUM GR AVIT Y AND COSMOLOGY?

TIME

Y

BIG BANG

A c c o r d i n g to t h e bi g b a n g m od el , t h e u n i v e r se d e v el o ped f r o m a n e x t r e m el y d e n se a n d h o t st ate.

Sp a c e it sel f h a s bee n e x p a n d i n g e v e r s i n c e, c a r r y i n g ga l a x i e s (a n d a l l o t h e r m at te r w it h it .

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WHAT’S BEFORE THE BIG BANG ?

It seems fairly likely that there was a Big Bang. The obvious question that could be asked to challenge or define the boundaries between physics and metaphysics is: what came before the Big Bang? + Physicists def ine the boundaries of physics by trying to describe them theoretically and then testing that description against observation. Our observed expanding Universe is very well described by flat space, with critical density supplied mainly by dark matter and a cosmological constant, that should expand forever. + If we follow this model backwards in time to when the Univer se was ver y hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental understanding of particle physics starts to poop out after the energy scale of electroweak unif ication, and theoretical p h y sic i s t s h a v e t o r e ac h f or m o de l s o f p ar t ic le p h y sic s b e y ond t h e S t an d ar d Model, to Gr and Unif ied T heor ie s, super sy mme t r y, st r ing t heor y and quant um cosmology.+ If we follow this model backwards in time to when the Universe was very hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental under standing of par ticle physics star ts to poop out after the energy scale of elec t r owe ak unif ic ation, and t heor e tic al phy sicist s have to r e ach for models o f p a r t i c l e p h y s i c s b e y o n d t h e S t a n d a r d M o d e l , t o G r a n d U n i f i e d T h e o r i e s, super symmetr y, string theor y and quantum cosmology. + A big complicating fac tor in under st anding st r ing c osmolog y is under st anding st r ing t heor ie s.

St r ing t heor ie s and M t heor y appe ar to be limi ting c ase s of some bigger, mor e fundament al t heor y. Until t hat’s sor ted ou t, any t hing we t hink we k now today is potentially up for grabs.

1. CAN STRING THEORY MAKE ANY COSMOLOGICAL PREDICTIONS RELEVANT TO BIG BANG PHYSICS? 2.

WHAT HAPPENS TO THE EX TR A DIMENSIONS? 3. IS THERE INFL ATION IN STRING THEORY? 4. WHAT CAN STRING THEORY TELL US ABOUT QUANTUM GR AVIT Y AND COSMOLOGY?

TIME

Y

BIG BANG

A c c o r d i n g to t h e bi g b a n g m od el , t h e u n i v e r se d e v el o ped f r o m a n e x t r e m el y d e n se a n d h o t st ate.

Sp a c e it sel f h a s bee n e x p a n d i n g e v e r s i n c e, c a r r y i n g ga l a x i e s (a n d a l l o t h e r m at te r w it h it .

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IS IT REAL ?

DIRECTLY OBSERVING STRINGS IS FAR BEYOND OUR CAPABILITIES NOW AND FOR THE FAR FUTURE. STRING THEORY'S DIVERSIT Y MAKES IT DIFFICULT TO DERIVE AN Y CLEAR PREDICTIONS THAT APPLY TO ALL VERSIONS. STRING THEORY HAS ITS SUPPORTERS AND ITS GAINSAYERS A MONG THEORETIC A L PH Y SICISTS. EVEN ADVOCATES ADMIT THAT THE THEORY COULD BE ENTIRELY WRONG.

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34 DIMENSION

A FRESH START

What is beyond question, is that even if one accepts the debatable reasoning of the staunch reductionist, principle is one thing and practice quite another. Almost everyone agrees that finding string theory would in no way mean t hat psycholog y, biolog y, geolog y, chemist r y, or even physics had been solved or in some sense subsumed. The universe is such a wonderfully rich and complex place t h a t t h e di s c o v e r y o f t h e f in al t h e or y, in t h e s e n s e w e ar e de s c r ibin g h e r e, w o uld n o t s p e ll t h e e n d o f science. + Quite the contrary: The discovery of string theory, the ultimate explanation of the universe at i t s most micr osc opic level, a t heor y t hat doe s not rely on any deeper explanation—would provide the f irmest foundation on which to build our understanding of the world. Its discovery would mark a beginning, not an end. The ultimate theory would provide an unshakable pillar of coherence forever assuring us that the universe is a comprehensible place.

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WHETHER OR NOT STRINGS ARE VALIDATED AS A "THEORY OF EVERYTHING," THEY PROVIDE A UNIQUE SET OF TOOLS TO UNDERSTAND AND EXPLORE THE DEEP STRUCTURE OF REALITY.

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39 TITLE V I A SMOO T H, P U R E W H I T E , 10 0 T E X T, P M S 15 8 O R A N G E

5&6 V I A L I N E N, P U R E W H I T E , 10 0 C O V E R , FOU R COL OR P R OC E SS, SPOT GLOSS VA R NISH.

13 & 14 V I A F E L T, W I L L O W, 80 COV ER , PMS 8402, SPOT DR Y VA R NISH.

21 & 2 2 V IA V ELLUM, WA R M W HITE, 65 COV ER , FOU R COL OR P R OC E SS

29 & 30 V I A S AT I N, WA R M W HITE, 65 COV ER , FOU R COL OR P R OC E SS

37 & 38 V I A S AT I N, WA R M W HITE, 65 COV ER , FOU R COL OR P R OC E SS

INFO V I A S M O O T H , I V O R Y, 24L B. FOU R COL OR P R OC E SS

3&4 V I A L I N E N, N AT RU A L , 65 COV ER . FOUR COL OR P R OC E SS, P MS 15 8 O R A N G E ,

11 & 12 V I A F E L T, C O O L W HITE, 65 COV ER .

FOUR COLOR P R OC E SS, SPO T GL OSS VA R NISH. 19 & 2 0 VIA V ELLUM, PURE W H I T E , 7 0 T E X T. F O U R COL OR P R OC E SS, SPO T GLOSS VA R NISH.

27 & 28 V I A S AT I N, BR IGH T W H I T E , 8 0 T E X T. P M S 032, SPOT GLOSS VA R NISH.

35 & 36 V I A S AT I N, BR IGH T W H I T E , 8 0 T E X T. P M S 032, SPOT GLOSS VA R NISH.

IN T ERIOR PA GE

V I A L A ID, NAT UR A L , 80 CO V ER , FOUR COLOR P R O C E S S , P M S 15 8 O R A N G E .

COV ER

39 & 40 V I A S AT I N, BR IGH T W H I T E , 8 0 T E X T. P M S 032, SPOT GLOSS VA R NISH.

31 & 3 2 V I A S AT I N, BR IGH T W H I T E , 8 0 T E X T. P M S 032, SPOT GLOSS VA R NISH.

23 & 24 VIA V ELLUM, PURE W H I T E , 7 0 T E X T. F O U R COL OR P R OC E SS, SPO T GLOSS VA R NISH.

15 & 16 V I A F E L T, W I L L O W, 80 COV ER , PMS 8402, SPOT DR Y VA R NISH.

7&8 V I A L N I E N, C Y A N, 80 COV ER . FOUR COLOR P R OC E SS, SPO T GL OSS VA R NISH.

COP Y RIGH T & IN T RO V I A SMOO T H, L IGH T G R A Y, 7 0 T E X T. F O U R COL OR P R OC E SS, SPO T GLOSS VA R NISH.

41 & 4 2 V I A S AT I N, WA R M W HITE, 65 COV ER , FOU R COL OR P R OC E SS, P M S 15 8 O R A N G E

33 & 34 V I A S AT I N, WA R M W HITE, 65 COV ER , FOU R COL OR P R OC E SS, P M S 15 8 O R A N G E

25 & 26 V I A SMOO T H, L IGH T G R A Y, 7 0 T E X T. F O U R COL OR P R OC E SS, PMS 032.

17 & 18 V I A F E L T, C O O L W H I T E , 65 COV ER . FOUR COL OR P R OC E SS

9 & 10 V I A L I N E N, SOF T C R E A M , 7 0 T E X T. F O U R COL OR P R OC E SS,

1&2 V I A SMOO T H, L IGH T G R A Y, 7 0 T E X T. F O U R COL OR P R OC E SS,

PRODUCTION NOTES

INFO

7&8

TITLE

9 & 10

19 & 2 0

31 & 3 2

COP Y RIGH T & IN T RO

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21 & 2 2

33 & 34

1&2

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35 & 36

3&4

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41 & 4 2

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Typeface: Blender, ChollasSlab, Samson Paper: Epson Premium Presentation Paper Program: Illustrator, InDesign, Photoshop Printer: MegaPix Imaging Bindery: California Office Service Photography: Swin Huang

COLOPHON

TEL: 1-800-THE MILL www.mohawkpaper.com

465 Saratoga Street Cohoes, N Y 12047

MOHAWK PINE PAPERS INC.

FOR MOST OF US, OR PERHAPS ALL OF US, IT’S IMPOSSIBLE TO IMAGINE A WORLD CONSISTING OF MORE THAN THREE SPATIAL DIMENSIONS.