Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension

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HYPERSPACE

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HYPERSPACE

A Scientific Odyssey Through Parallel Universes, Time Warps, and The Tenth Dimension Michio Kak u Illustrations by Robert O'Keefe

New Yor k Oxfor d OXFORD UNIVERSIT Y PRESS 1994

Oxford Universit y Press Oxiford Ne w York Toront o Delhi Bomba y Calcutt a Madra s Karach i Kuala Lumpur Singapor e Hon g Kong Toky o Nairobi Da r es Salaam Cap e Tow n Melbourne Aucklan d Madri d and associate d companie s in Berlin Ibada n

Copyright © 199 4 b y Oxford Universit y Press, Inc . Published b y Oxford Universit y Press, Inc. , 200 Madison Avenue , New York, New York 1001 6 Oxford i s a registere d trademar k o f Oxford Universit y Press All rights reserved. N o part o f this publication ma y be reproduced, stored i n a retrieva l system, or transmitted , in an y form o r b y any means, electronic, mechanical, photocopying, recording , o r otherwise, without th e prio r permissio n of Oxford Universit y Press . Library of Congress Cataloging-in-Publicatio n Dat a Kaku, Michio. Hypcrspacc : a scientifi c odyssc y through paralle l universes, time warps, and the tent h dimensio n / Miehio Kaku. p. cm . Includes bibliographica l references an d index . ISBN 0-19-508514- 0 1. Katu/a-Klei n theories . 2 . Supcrstring theories. 3. Hyperspace. I . Title. QC793.3.F5K35 199 4 530. 1 '42—dc20 93-791 0 "Cosmic Gall. " From Telephone. Poles and Other Poems by John Updike . Copyright © 196 0 byjoh n Updike . Reprinted b y permission o f Alfred A . Knopf, Inc. Originally appeared i n Th e New Yorker. Excerpt fro m "Fir e an d Ice. " Fro m Th e Poetry o f Robert Frost, edited b y Edward Conner y Lathem . Copyright 195 1 b y Robert Frost . Copyright 1923 , © 196 9 b y Henry Holt , avid Company , inc . Reprinted b y permission o f Henr y Holt an d Company, Inc .

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Printed i n th e Unite d States of America on acid-fre e pape r

This boo k i s dedicated to m y parents

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Preface

Scientific revolutions , almost by definition, def y commo n sense . If al l ou r common-sens e notion s abou t th e univers e wer e correct , then scienc e would have solved the secret s o f the univers e thousands of years ago. The purpos e o f science is to peel back the layer of the appear ance o f objects to reveal their underlyin g nature. I n fact , i f appearanc e and essenc e were th e same thing , ther e woul d be no nee d for science. Perhaps th e mos t deepl y entrenche d common-sens e notio n abou t our worl d i s tha t i t i s thre e dimensional . I t goe s withou t saying tha t length, width, and breadt h suffic e t o describ e al l objects in ou r visibl e universe. Experiments with babies an d animal s have shown that we are born wit h a n innat e sens e tha t ou r worl d i s thre e dimensional . I f we include time as another dimension , then fou r dimension s are sufficien t to recor d al l events in th e universe . No matte r wher e ou r instrument s have probed , fro m dee p within the ato m t o the farthes t reaches o f the galactic cluster, we have onl y found evidenc e of these fou r dimensions . To claim otherwis e publicly , tha t other dimensions might exist o r that our univers e ma y coexist with others, is to invite certain scorn . Yet this deeply ingraine d prejudic e abou t ou r world , firs t speculate d o n b y ancient Gree k philosophers 2 millennia ago, is about to succumb to th e progress o f science. This book is about a scientific revolution created by the theory o f hyperspace,1 whic h states that dimensions exist beyond the commonly accepted four o f spac e an d time . Ther e i s a growin g acknowledgmen t amon g physicists worldwide, including several Nobel laureates, that the universe may actuall y exist in higher-dimensiona l space . I f this theor y i s proved correct, i t will creat e a profound conceptua l an d philosophica l revolu tion in our understandin g o f the universe. Scientifically, th e hyperspac e theory goe s b y the name s of Kaluza-Klein theor y and supergravity . But

viii Preface its mos t advanced formulatio n is called superstrin g theory , which even predicts th e precise number of dimensions: ten. The usual three dimensions o f spac e (length , width, and breadth ) an d on e o f tim e ar e no w extended b y six more spatia l dimensions. We caution tha t th e theor y o f hyperspac e ha s no t ye t been experi mentally confirmed and would , in fact, be exceedingly difficult t o prove in the laboratory. However, the theory has already swept across the majo r physics researc h laboratorie s o f th e worl d an d ha s irrevocabl y altered the scientific landscape of modern physics, generating a staggering number o f researc h paper s i n th e scientifi c literatur e (ove r 5,00 0 b y on e count). However, almost nothing ha s been writte n for th e la y audience to explai n th e fascinatin g propertie s o f higher-dimensiona l space . Therefore, th e genera l publi c is only dimly aware, if at all , of this revolution. In fact , th e glib references to other dimension s an d paralle l universes i n th e popula r cultur e ar e ofte n misleading . Thi s i s regrettabl e because th e theory' s importanc e lie s i n it s powe r t o unif y al l known physical phenomen a i n a n astonishingl y simple framework . This boo k makes available, for th e first time, a scientifically authoritative but accessible account o f the curren t fascinatin g research o n hyperspace . To explain why the hyperspac e theory has generated s o much excitement within the world of theoretical physics , I have developed fou r fundamental theme s tha t run throug h thi s book lik e a thread. Thes e fou r themes divide the boo k int o fou r parts. In Par t I, I develop th e earl y history of hyperspace, emphasizing the theme tha t th e law s of nature becom e simple r an d mor e elegan t when expressed i n higher dimensions . To understan d ho w adding highe r dimension s can simplif y physical problems, conside r th e followin g example : T o th e ancien t Egyptians, the weathe r was a complete mystery . What caused th e seasons ? Why did it get warmer as they traveled south? Why did th e wind s generally blow in one direction? The weather was impossible to explain from the limited vantage point of the ancient Egyptians, to whom the earth appeared flat , like a two-dimensional plane. But now imagine sending the Egyptians in a rocke t int o oute r space , where the y can se e th e eart h a s simple and whole in its orbit aroun d th e sun . Suddenly, the answer s to thes e ques tions become obvious . From oute r space , i t i s clear tha t th e earth' s axi s i s tilted abou t 2 3 degrees from th e vertical (th e 'vertical " bein g th e perpendicular t o the plane of the earth's orbit around th e sun). Because of this tilt, the north ern hemispher e receive s much less sunlight during on e par t of its orbit than during another part. Hence we have winter and summer. And since

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the equator receive s more sunligh t then th e northern o r southern pola r regions, it becomes warmer as we approach th e equator . Similarly , since the eart h spin s counterclockwise to someone sittin g on th e nort h pole , the cold , pola r ai r swerve s as it move s south towar d th e equator . Th e motion o f hot an d col d masse s of air, set in motion b y the earth' s spin, thus help s t o explai n wh y the wind s generall y blo w in on e direction , depending o n where you are on th e earth . In summary, the rather obscure laws of the weather are easy to understand onc e we view the earth from space. Thus th e solution t o the prob lem is to go u p into space, into the third dimension. Facts that were impossible t o understan d i n a fla t worl d suddenl y becom e obviou s whe n viewing a three-dimensional earth . Similarly, th e law s o f gravit y and ligh t seem totall y dissimilar. They obey differen t physica l assumption s an d differen t mathematics . Attempts t o splic e thes e tw o force s hav e alway s failed . However, if we add one mor e dimension , a fifth dimension, to the previous four dimensions of space an d time , then th e equation s governin g light and gravity appear t o merg e togethe r lik e tw o pieces o f a jigsaw puzzle . Light , i n fact, ca n b e explaine d a s vibrations i n th e fift h dimension . I n thi s way, we see tha t th e law s of light and gravit y become simple r in fiv e dimen sions. Consequently, many physicists are now convinced that a conventional four-dimensional theor y is "too small " to describe adequately the forces that describe ou r universe . In a four-dimensional theory , physicists have to squeeze together th e forces of nature i n a clumsy, unnatural fashion . Furthermore, this hybrid theory is incorrect. Whe n expressed i n dimen sions beyon d four , however , w e hav e "enoug h room " t o explai n th e fundamental force s in an elegant , self-containe d fashion. In Part II, we further elaborate o n thi s simple idea, emphasizing tha t the hyperspac e theor y may be able to unify all known laws of nature int o one theory . Thu s th e hyperspac e theor y ma y be th e crownin g achieve ment o f 2 millenni a o f scientifi c investigation : th e unificatio n o f al l known physical forces. It may give us the Hol y Grail of physics, the "the ory of everything" tha t elude d Einstei n for s o many decades . For th e pas t half :century, scientists have been puzzle d as to why the basic force s tha t hol d togethe r th e cosmos—gravity , electromagnetism, and th e stron g an d wea k nuclear forces—diffe r s o greatly. Attempts by the greatest mind s of the twentieth century to provide a unifying pictur e of al l th e know n force s hav e failed . However , th e hyperspac e theor y allows th e possibilit y of explainin g th e fou r force s o f natur e a s well a s the seemingly random collectio n of subatomic particles in a truly elegant

X Preface

fashion. I n th e hyperspac e theory , "matter " ca n b e als o viewed as th e vibrations that ripple through th e fabric of space and time. Thus follow s the fascinatin g possibilit y that everythin g we see aroun d us , fro m th e trees an d mountain s to th e star s themselves, are nothin g but vibrations in hyperspace. I f thi s i s true, the n thi s give s u s a n elegant , simple , an d geometric mean s o f providing a coherent an d compellin g descriptio n of the entir e universe. In Par t III , we explore th e possibilit y that, unde r extrem e circum stances, spac e ma y be stretche d unti l i t rip s o r tears . I n othe r words , hyperspace ma y provide a mean s t o tunne l throug h spac e an d time . Although we stress that thi s is still highly speculative, physicists are seriously analyzing the propertie s o f "wormholes, " o f tunnels that link distant parts of space and time . Physicists at the California Institute of Technology, for example, hav e seriously proposed the possibilit y of building a tim e machine , consistin g o f a wormhole tha t connect s th e pas t wit h the future . Time machine s hav e now left th e real m o f speculation an d fantasy an d hav e become legitimat e fields of scientific research . Cosmologists hav e eve n propose d th e startlin g possibilit y tha t ou r universe i s just on e amon g a n infinit e numbe r o f paralle l universes . These universes might be compared to a vast collection of soap bubbles suspended i n air . Normally , contact betwee n thes e bubbl e universe s is impossible, but , b y analyzin g Einstein' s equations , cosmologist s hav e shown that there might exist a web of wormholes, or tubes, that connec t these paralle l universes . On eac h bubble , we can defin e our own distinctive space and time , which have meaning onl y on its surface; outsid e these bubbles , space and tim e have no meaning . Although man y consequences o f this discussion ar e purel y theoretical, hyperspac e trave l may eventually provide th e mos t practica l application of all: to sav e intelligent life , includin g ours , from the deat h of the universe . Scientists universally believe tha t th e univers e must eventually die, an d wit h i t all life tha t ha s evolve d over billions of years. For example, accordin g to the prevailin g theory, called the Big Bang, a cosmic explosio n 1 5 to 2 0 billio n year s ag o se t th e univers e expanding , hurling star s and galaxie s awa y from us at grea t velocities. However, if the univers e on e da y stop s expandin g an d begin s t o contract , i t wil l eventually collapse into a fiery cataclysm called the Big Crunch, in which all intelligent life wil l be vaporized by fantastic heat. Nevertheless, some physicists hav e speculate d tha t th e hyperspac e theor y ma y provide th e one an d onl y hope of a refuge for intelligent life. I n th e las t seconds of the deat h o f ou r universe , intelligen t lif e ma y escape th e collaps e by fleeing into hyperspace.

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In Part IV , we conclude wit h a final, practical question: If the theor y is proved correct, then when will we be able t o harness th e powe r o f the hyperspace theory? This is notjust a n academic question, because i n the past, th e harnessin g o f just one o f the fou r fundamenta l forces irrevo cably changed th e course of human history, lifting us from th e ignoranc e and squalo r o f ancient, preindustrial societie s to modern civilization . In some sense , eve n th e vas t sweep o f huma n histor y can b e viewe d i n a new light, in terms of the progressiv e mastery of each of the fou r forces. The histor y of civilization has undergone a profound chang e a s each of these force s was discovered an d mastered . For example , whe n Isaa c Newto n wrot e dow n th e classica l laws o f gravity, h e develope d th e theor y o f mechanics, which gave us th e law s governing machines. This, in turn, greatly accelerated th e Industrial Revolution, whic h unleashed politica l force s that eventually overthrew th e feudal dynasties of Europe. I n the mid-1860s, when James Clerk Maxwell wrote down the fundamenta l law s of the electromagneti c force , he ushered i n th e Electri c Age, which gave u s th e dynamo , radio, television , radar, household appliances , the telephone, microwaves , consumer electronics, the electronic computer , lasers, and many other electroni c marvels. Without th e understandin g an d utilizatio n o f the electromagneti c force, civilizatio n would have stagnated, froze n i n a time befor e th e discovery of the ligh t bulb an d th e electri c motor. I n th e mid-1940s , when the nuclea r forc e wa s harnessed, th e worl d wa s again turne d upsid e down wit h th e developmen t o f th e atomi c an d hydroge n bombs , th e most destructive weapons on the planet. Because we are riot on the verge of a unifie d understandin g o f all the cosmi c force s governing th e uni verse, one migh t expect tha t any civilization that masters the hyperspac e theory will become lor d o f the universe . Since th e hyperspac e theor y is a well-defined body of mathematical equations, w e can calculat e th e precis e energ y necessar y to twis t spac e and tim e int o a pretze l or t o creat e wormhole s linking distant parts of our universe . Unfortunately , the result s ar e disappointing . Th e energ y required fa r exceed s anythin g tha t ou r plane t ca n muster . In fact , th e energy i s a quadrillion times larger tha n th e energ y of our larges t ato m smashers. We must wait centuries or even millennia until our civilization develops th e technica l capability of manipulating space—time , o r hop e for contac t wit h a n advance d civilizatio n tha t ha s alread y mastere d hyperspace. Th e boo k therefor e end s b y exploring th e intriguin g bu t speculative scientifi c question o f wha t leve l o f technolog y i s necessary for u s to become masters o f hyperspace . Because the hyperspace theory takes us far beyond normal, common-

xii Preface sense conception s o f spac e an d time , I hav e scattere d throughou t th e text a few purely hypothetical stories . I was inspired t o utiliz e thi s pedagogical techniqu e b y th e stor y o f Nobe l Priz e winne r Isidor e I . Rab i addressing a n audienc e o f physicists. He lamente d th e abysma l state of science educatio n i n th e Unite d State s an d scolde d th e physic s com munity for neglectin g it s duty in popularizin g th e adventur e o f science for th e genera l publi c and especiall y for the young . In fact , h e admon ished, science-fictio n writer s ha d don e mor e t o communicat e th e romance o f science than al l physicists combined. In a previou s book, Beyond Einstein: Th e Cosmic Quest for th e Theory o f the Universe (coauthore d wit h Jennifer Trainer) , I investigate d super string theory, described th e nature o f subatomic particles, and discusse d at length the visible universe and ho w all the complexitie s of matter might be explaine d b y tiny, vibrating strings. In thi s book, I have expanded o n a differen t them e an d explore d th e invisible universe—that is, the worl d of geometry and space-time . The focu s o f this book i s not th e natur e o f subatomic particles , bu t th e higher-dimensiona l worl d i n whic h the y probably live . I n th e process , reader s wil l se e tha t higher-dimensiona l space, instead of being an empty , passive backdrop agains t which quarks play ou t thei r eterna l roles , actuall y becomes th e centra l acto r i n th e drama o f nature. In discussing the fascinatin g history of the hyperspac e theory, we will see tha t th e searc h fo r th e ultimat e natur e o f matter , begu n b y th e Greeks 2 millennia ago , ha s bee n a lon g an d tortuou s one . Whe n th e final chapte r i n thi s long sag a is written b y future historians o f science, they ma y well recor d tha t th e crucia l breakthrough wa s the defea t o f common-sense theorie s o f three o r fou r dimension s an d th e victor y of the theor y o f hyperspace. New York M.K

May 1993

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Acknowledgments

In writin g this book, I hav e been fortunat e t o hav e Jeffrey Robbin s as my editor. He was the editor who skillfully guided the progress of three of my previous textbooks i n theoretica l physic s written for th e scientific community, concerning the unified field theory, superstring theory, and quantum fiel d theory . This book, however , marks th e first popular science boo k aime d a t a general audienc e tha t I have written for him . It has always been a rare privileg e to work closely with him. I would als o like to than k Jennife r Trainer, wh o has been m y coauthor o n tw o previous popular books . Onc e again , sh e ha s applied he r considerable skill s to make the presentatio n a s smooth an d coheren t as possible. I a m als o gratefu l t o numerou s othe r individual s who hav e helpe d to strengthe n an d criticiz e earlier draft s o f thi s book : Bur t Solomon , Leslie Meredith, Eugene Mallove , and m y agent, Stuart Krichevsky. Finally, I woul d lik e t o than k th e Institut e fo r Advance d Stud y at Princeton, where muc h o f this book wa s written, for it s hospitality. The Institute, where Einstein spent th e las t decades o f his life, was an appro priate plac e t o writ e abou t th e revolutionar y development s tha t hav e extended an d embellishe d much o f his pioneering work.

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Contents

Part I Enterin g the Fifth Dimensio n 1. World s Beyond Spac e an d Time , 3 2. Mathematician s and Mystics , 30 3. Th e Ma n Who "Saw " th e Fourt h Dimension, 55 4. Th e Secre t o f Light: Vibrations i n th e Fift h Dimension , 8 0

Part I I Unificatio n in Ten Dimensions 5. Quantu m Heresy , 111 6. Einstein' s Revenge , 136 7. Superstrings , 151 8. Signal s from th e Tent h Dimension, 178 9. Befor e Creation , 19 1

xvi Contents Part II I Wormholes : Gateway s t o Anothe r Universe ? 10. Blac k Holes and Paralle l Universes , 21 7 11. T o Buil d a Time Machine , 232 12. Collidin g Universes, 252

Part I V Master s o f Hyperspac e 13. Beyon d th e Future , 273 14. Th e Fat e of th e Universe , 301 15. Conclusion , 31 3 Notes, 33 5 References an d Suggested Reading , 353 Index, 35 5

PART I Entering the Fift h Dimensio n

But the creative principle resides in mathematics. In a certain sense, therefore , I hol d i t tru e tha t pur e though t ca n gras p reality, as the ancient s dreamed . Albert Einstein

1 Worlds Beyon d Space and Time I want to know how God created this world. I am not intereste d in thi s or that phenomenon. I want to know His thoughts, th e rest are details . Albert Einstein

The Educatio n of a Physicist

T

WO incidents from m y childhood greatl y enriched m y understanding o f th e worl d an d sen t m e o n cours e t o becom e a theoretica l physicist. I remembe r tha t m y parents woul d sometimes take m e t o visi t th e famous Japanese Te a Garde n i n Sa n Francisco . On e o f m y happies t childhood memorie s i s of crouching nex t to th e pond , mesmerize d by the brilliantl y colored car p swimming slowly beneath th e water lilies. In thes e quie t moments, I felt fre e t o le t m y imagination wander ; I would ask myself silly questions that a only child might ask, such as how the car p i n tha t pon d woul d view th e worl d aroun d them . I thought , What a strange world theirs must be! Living their entir e live s in th e shallo w pond, th e car p would believe that their "universe" consiste d of the murky water and th e lilies. Spending most of their tim e foraging on th e botto m o f the pond , the y would be onl y dimly aware that a n alie n worl d could exis t above th e surface.

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4 ENTERIN

G TH E FIFTH DIMENSIO N

The natur e o f m y worl d wa s beyon d thei r comprehension . I wa s intrigued that I could sit only a few inches from th e carp, yet be separated from the m b y an immense chasm . The car p an d I spent our lives in two distinct universes, never enterin g each other' s world, yet were separated by only the thinnes t barrier, th e water' s surface. I onc e imagine d tha t ther e ma y be car p "scientists " livin g among the fish . The y would , I thought , scof f a t an y fish who propose d tha t a parallel world could exist just above the lilies . To a carp "scientist, " th e only thing s tha t were rea l wer e what the fis h coul d se e o r touch . Th e pond wa s everything. An unseen worl d beyon d th e pon d mad e n o scientific sense . Once I was caught in a rainstorm. I noticed that the pond's surfac e was bombarde d b y thousand s o f tin y raindrops . Th e pond' s surfac e became turbulent , and th e wate r lilies were being pushe d i n al l directions by water waves. Taking shelter from th e wind and th e rain , I wondered ho w all this appeared t o the carp . To them, the water lilies would appear t o b e movin g aroun d b y themselves, without anythin g pushing them. Sinc e th e wate r the y lived i n woul d appea r invisible , much lik e the ai r and spac e around us , they would be baffle d tha t th e wate r lilies could mov e around b y themselves. Their "scientists, " I imagined , woul d concoc t a cleve r inventio n called a "force " i n orde r t o hid e thei r ignorance . Unabl e t o compre hend tha t ther e coul d be waves on th e unsee n surface , they would conclude that lilies could move without being touched because a mysterious, invisible entity called a force acted betwee n them . They might give this illusion impressive, lofty name s (suc h as action-at-a-distance, or th e ability of the lilie s to move without anything touching them) . Once I imagined wha t would happe n i f I reache d dow n an d lifte d one o f the car p "scientists " ou t o f the pond . Befor e I threw him back into the water, he migh t wiggle furiously as I examined him . I wondered how thi s would appea r t o th e res t o f the carp . T o them , i t would be a truly unsettling event. They would first notice that on e o f their "scien tists" ha d disappeare d fro m thei r universe . Simpl y vanished, without leaving a trace. Whereve r they would look, there woul d be no evidence of the missin g carp i n their universe. Then, second s later, when I threw him back into th e pond, th e "scientist " would abruptly reappear ou t of nowhere. T o th e othe r carp , i t would appea r tha t a miracl e ha d hap pened. After collectin g his wits , th e "scientist " woul d tel l a trul y amazin g story. "Withou t warning, " h e woul d say, "I wa s somehow lifted ou t o f the universe (the pond) an d hurled into a mysterious nether world, with

Worlds Beyond Space and Time 5 blinding lights and strangely shaped object s that I had never seen before . The stranges t o f all was the creatur e wh o held m e prisoner, wh o did no t resemble a fish in th e slightest . I was shocked t o see that i t had n o fins whatsoever, but nevertheless coul d mov e without them. It struck me that the familiar laws of nature n o longer applie d i n this nether world . Then , just a s suddenly, I found mysel f thrown bac k int o ou r universe. " (Thi s story, o f course, o f a journey beyond th e univers e would be s o fantastic that mos t o f the car p woul d dismiss it as utter poppycock. ) I often thin k that we are like the car p swimmin g contentedly i n tha t pond. We live out ou r live s in our ow n "pond," confident that our universe consist s of onl y thos e thing s w e can se e o r touch . Lik e th e carp , our univers e consist s o f onl y th e familia r an d th e visible . W e smugly refuse t o admi t tha t paralle l universe s o r dimension s ca n exis t nex t t o ours, just beyond ou r grasp . If our scientist s invent concepts like forces, it i s only because the y canno t visualiz e the invisibl e vibrations tha t fill the empt y spac e aroun d us . Som e scientist s snee r a t th e mentio n o f higher dimension s becaus e the y canno t b e convenientl y measured i n the laboratory . Ever since that time, I have been fascinated by the possibility of other dimensions. Lik e mos t children , I devoured adventur e storie s i n which time traveler s entere d othe r dimension s an d explore d unsee n paralle l universes, wher e th e usua l law s o f physic s coul d b e convenientl y suspended. I grew up wondering i f ships that wandered int o th e Bermud a Triangle mysteriousl y vanished int o a hole i n space; I marveled a t Isaa c Asimov's Foundation Series , i n which the discover y of hyperspace travel led t o the ris e o f a Galactic Empire . A secon d inciden t fro m m y childhoo d als o mad e a deep , lastin g impression o n me . Whe n I was 8 years old, I heard a stor y that woul d stay with me for the res t of my life. I remember m y schoolteachers tellin g the clas s abou t a grea t scientis t who ha d just died . The y talke d abou t him with great reverence , callin g him one o f the greatest scientist s in all history. They said tha t ver y few people coul d understan d hi s ideas, bu t that his discoveries changed th e entir e world and everythin g around us . I didn' t understan d muc h o f what they were tryin g to tel l us , but wha t most intrigue d m e abou t thi s ma n wa s that h e die d befor e h e coul d complete hi s greatest discovery . They said he spent years on this theory , but h e die d with his unfinished papers stil l sitting on hi s desk. I wa s fascinated b y th e story . T o a child , thi s wa s a grea t mystery . What wa s his unfinishe d work ? What wa s in thos e paper s o n hi s desk? What proble m coul d possibl y be so difficult an d s o important tha t suc h a great scientis t would dedicate year s of his life t o its pursuit? Curious, I

6 ENTERIN

G T H E F I F T H D I M E N S I ON

decided t o lear n al l I coul d abou t Alber t Einstei n and hi s unfinished theory. I still have warm memories of spending many quiet hours reading every book I could fin d abou t thi s grea t ma n an d hi s theories. Whe n I exhausted th e book s i n our loca l library, I began t o scour libraries and bookstores acros s th e city , eagerl y searchin g fo r mor e clues . I soo n learned tha t thi s story was far mor e excitin g tha n an y murder mystery and mor e importan t tha n anythin g I could ever imagine. I decided tha t I would try to get t o th e roo t of this mystery, even if I had t o become a theoretical physicis t to do it. I soon learne d tha t the unfinished papers on Einstein's desk were an attempt t o construc t wha t he calle d th e unifie d fiel d theory , a theor y that coul d explai n al l the law s o f nature , fro m th e tinies t atom t o th e largest galaxy. However, being a child, I didn't understand tha t perhaps there was a link between the car p swimming in the Tea Garden an d th e unfinished paper s lyin g on Einstein' s desk . I didn' t understan d tha t higher dimension s might be th e ke y to solving the unifie d field theory. Later, in high school, I exhausted mos t of the local libraries and often visited th e Stanfor d Universit y physics library. There, I came acros s th e fact tha t Einstein' s work made possibl e a new substance calle d antimatter, whic h would ac t lik e ordinar y matte r bu t woul d annihilat e upo n contact wit h matter i n a burs t of energy. I also read tha t scientist s had built larg e machines , o r "ato m smashers, " tha t coul d produc e micro scopic quantities of this exotic substance in th e laboratory . One advantag e of youth is that it is undaunted b y worldly constraints that woul d ordinarily seem insurmountabl e t o most adults . Not appre ciating the obstacle s involved, I set out t o build m y own atom smasher . 1 studied th e scientifi c literatur e until I was convinced that I could build what was called a betatron, whic h could boos t electron s t o million s of electron volts . ( A million electro n volt s i s the energ y attaine d b y electrons accelerated b y a field of a million volts.) First, I purchased a small quantity of sodium-22, which is radioactive and naturall y emits positrons (th e antimatter counterpar t of electrons). Then 1 built wha t is called a clou d chamber , whic h makes visible the tracks left by subatomic particles. I was able to take hundreds of beautiful photographs o f the track s left behin d b y antimatter. Next , I scavenge d around larg e electronic warehouses in the area, assembled the necessary hardware, including hundreds of pounds o f scrap transformer steel, and built a 2.3-million-electron-volt betatron i n my garage that would be powerful enough to produce a beam of antielectrons. To construct the monstrous magnet s necessar y fo r th e betatron , I convince d m y parents t o help me wind 22 miles of cooper wire on th e high-schoo l football field.

Worlds Beyond Space and Time 7

We spen t Christma s vacation o n th e 50-yar d line , winding and assem bling th e massiv e coil s tha t woul d ben d th e path s o f th e high-energ y electrons. When finall y constructed , th e 300-pound , 6-kilowat t betatro n con sumed every ounce o f energy my house produced . Whe n I turned i t on, I would usually blow every fuse, an d th e hous e woul d suddenl y becam e dark. Wit h th e hous e plunge d periodicall y int o darkness , m y mothe r would ofte n shak e he r head . ( I imagined tha t sh e probabl y wondere d why she couldn't hav e a child who played baseball or basketball, instead of building these hug e electrica l machines in the garage. ) I was gratified that th e machin e successfull y produce d a magneti c fiel d 20,00 0 time s more powerfu l tha n th e earth' s magneti c field , whic h i s necessary t o accelerate a beam o f electrons. Confronting th e Fift h Dimensio n Because my family was poor, m y parents wer e concerned tha t I wouldn't be able to continue m y experiments and m y education. Fortunately, the awards tha t I won for m y various scienc e project s caught th e attentio n of the atomi c scientist Edward Teller. Hi s wife generousl y arranged fo r me t o receiv e a 4-year scholarship t o Harvard , allowin g me t o fulfill m y dream. Ironically, although a t Harvar d I began m y formal training in theo retical physics, it was also where my interest i n higher dimension s grad ually die d out . Lik e other physicists , I began a rigorou s an d thoroug h program o f studyin g the highe r mathematic s o f eac h o f th e force s of nature separately , in complete isolation from on e another. I still remember solvin g a proble m i n electrodynamic s for m y instructor, and the n asking him wha t the solutio n migh t look like if space were curved i n a higher dimension . H e looke d a t m e i n a strange way , as if I were a bi t cracked. Lik e others befor e me , I soon learne d t o put asid e m y earlier, childish notions about higher-dimensional space . Hyperspace, I was told, was not a suitable subject of serious study. I was never satisfied with this disjointed approach t o physics, and m y thoughts would often drift back to the the carp living in the Tea Garden . Although th e equation s we used fo r electricit y and magnetism , discovered by Maxwell in the nineteenth century , worked surprisingly well, the equations seeme d rathe r arbitrary . I fel t tha t physicist s (like th e carp ) invented thes e "forces " t o hide our ignoranc e o f how objects can move each othe r withou t touching .

8 ENTERIN

G TH E FIFTH DIMENSIO N

In m y studies, 1 learned tha t on e o f th e grea t debate s o f th e nine teenth centur y ha d bee n abou t ho w ligh t travel s throug h a vacuum . (Light from the stars, in fact, can effortlessly travel trillions upon trillions of miles through th e vacuu m o f outer space.) Experiment s als o showed beyond questio n tha t ligh t i s a wave . But i f ligh t wer e a wave , then i t would require something t o be "waving." Soundwave s require air, water waves require water , but sinc e there i s nothing to wave in a vacuum, we have a paradox. Ho w can ligh t be a wave if there is nothing t o wave? So physicists conjure d u p a substanc e calle d th e aether , whic h fille d th e vacuum and acte d a s the mediu m fo r light. However, experiments con clusively showed tha t th e "aether " does no t exist. * Finally, when I became a graduate studen t in physics at the University of California at Berkeley , I learned quit e b y accident tha t ther e was an alternative, albei t controversial , explanatio n o f ho w ligh t ca n trave l through a vacuum . Thi s alternativ e theor y wa s s o outlandis h tha t I received quit e a jolt whe n I stumbled acros s it . That shock was similar to th e on e experience d b y many Americans when the y first heard tha t President John Kennedy had bee n shot . They can invariably remember the precise moment whe n they heard th e shocking news, what they were doing, and t o whom they were talking at that instant. We physicists, too, receive quit e a shock when we first stumbl e across Kalu/a-Klein theor y for th e firs t time . Sinc e the theor y was considered t o be a wild specula tion, i t was never taugh t i n graduat e school ; s o young physicists are lef t to discover i t quite b y accident i n thei r casua l readings . This alternativ e theor y gave the simples t explanation o f light: that i t was really a vibration o f the fift h dimension , o r what used t o called th e fourth dimensio n b y the mystics . If light could trave l through a vacuum, it was because th e vacuu m itsel f was vibrating, becaus e th e "vacuum " really existe d i n fou r dimension s o f spac e an d on e o f time . B y adding the fift h dimension , th e forc e of gravity and ligh t coul d b e unifie d in a startlingly simple way. Looking bac k at my childhood experience s a t th e Tea Garden , I suddenly realize d tha t thi s was the mathematica l theor y for which I had bee n looking . The ol d Kaluza-Klein theory, however, had man y difficult, technica l problems tha t rendere d i t useless for ove r hal f a century. All this, however, ha s change d i n th e pas t decade . Mor e advance d version s o f th e theory, lik e supergravity theory an d especiall y superstring theory , have *Surprisingly, eve n toda y physicists stil l d o no t hav e a rea l answe r to thi s puzzle, bu t over th e decade s w e have simply gotte n use d t o th e ide a tha t ligh t can trave l through a vacuum eve n if there i s nothing to wave.

Worlds Beyond Space and Time 9

finally eliminated the inconsistencies of the theory . Rather abruptly, the theory of higher dimension s is now being champione d i n researc h laboratories aroun d th e globe . Man y of the world' s leading physicists now believe that dimensions beyond th e usua l four of space and tim e might exist. This idea, in fact, ha s become th e foca l point of intense scientifi c investigation. Indeed , man y theoretica l physicist s no w believ e tha t higher dimensions may be the decisive step in creating a comprehensiv e theory that unites the law s of nature—a theory of hyperspace. If it proves to be correct , the n futur e historian s o f science may well record that one of the great conceptual revolutions in twentieth-century science was the realization that hyperspace may be the key to unlock the deepest secret s of nature an d Creatio n itself . This seminal concept has sparked an avalanche of scientific research: Several thousan d paper s writte n b y theoretical physicist s i n th e majo r research laboratorie s around th e world have been devote d t o exploring the propertie s of hyperspace . The page s of Nuclear Physics and Physics Letters, tw o leading scientifi c journals, hav e bee n floode d wit h article s analyzing the theory . Mor e than 20 0 international physics conferences have been sponsored to explore the consequences of higher dimensions. Unfortunately, we are still far from experimentall y verifying tha t ou r universe exist s in highe r dimensions . (Precisel y what it woul d tak e t o prove th e correctnes s o f the theor y an d possibl y harness th e powe r of hyperspace wil l b e discusse d late r i n thi s book. ) However , this theor y has no w becom e firml y establishe d a s a legitimat e branc h o f moder n theoretical physics . The Institut e fo r Advance d Study at Princeton, fo r example, wher e Einstei n spen t th e las t decades o f his lif e (an d wher e this book was written), is now one of the activ e centers of research on higher-dimensional space-time . Steven Weinberg, who won the Nobe l Prize in physics in 1979 , summarized thi s conceptual revolutio n when h e commente d recentl y that theoretical physic s seems t o be becomin g mor e an d mor e lik e science fiction. Why Can't W e Se e Highe r Dimensions ? These revolutionar y idea s see m strang e a t firs t becaus e w e tak e fo r granted that our everyda y world has three dimensions . As the late physicist Heinz Pagels noted, "One featur e of our physical world is so obvious that most people are not even puzzled by it—the fact that space is threedimensional."1 Almost by instinct alone, we know that any object can be

10 E N T E R I N

G TH E F I F T H D I M E N S I O N

described b y giving it s height, width , and depth . B y giving three num bers, we can locat e an y position i n space . I f we want to mee t someon e for lunc h i n Ne w York, we say, "Meet me o n th e twenty-fourt h floor o f the building at the corner of Forty-second Street and First Avenue." Two numbers provid e us the street corner ; an d th e third , th e height off the ground. Airplane pilots , too, kno w exactly where the y are wit h thre e num bers—their altitude and tw o coordinates tha t locate thei r position o n a grid o r map . I n fact , specifyin g thes e thre e number s ca n pinpoin t any location in our world, from th e ti p of our nos e t o the end s of the visible universe. Even babies understand this : Tests with infants have shown that they will crawl to the edg e o f a cliff, pee r over the edge , and craw l back. In additio n t o understandin g "left " an d "right " an d "forward " an d "backward" instinctively , babie s instinctivel y understan d "up " an d "down." Thus the intuitive concept of three dimensions is firmly embedded i n our brain s fro m a n earl y age. Einstein extended thi s concept t o include time as the fourth dimension. For example, to meet that someone for lunch, we must specify tha t we shoul d mee t at , say , 12:30 P.M . i n Manhattan ; tha t is , t o specif y a n event, we also need t o describ e it s fourth dimension , the time at which the even t takes place. Scientists today are interested in going beyond Einstein's conception of the fourt h dimension. Current scientific interes t centers on th e fifth dimension (th e spatia l dimensio n beyon d tim e an d th e thre e dimen sions of space) and beyond . (T o avoid confusion, throughout thi s book I hav e bowe d t o custo m an d calle d th e fourt h dimensio n th e spatial dimension beyon d length , breadth , an d width . Physicists actually refer to thi s as the fift h dimension , but I will follo w historica l precedent. We will call time the fourt h temporal dimension.) How do we see the fourt h spatial dimension? The proble m is , we can't. Higher-dimensiona l space s are impossible to visualize ; s o it is futile eve n t o try . The prominen t Germa n physicist Hermann vo n Helmholt z compare d th e inabilit y to "see " th e fourt h dimension with th e inabilit y of a blind ma n t o conceive of the concep t of color. No matter how eloquently we describe "red" t o a blind person, words fail to impart the meaning of anything as rich in meaning as color. Even experience d mathematician s and theoretica l physicist s who have worked with higher-dimensional space s for years admit that they cannot visualize them. Instead, they retreat into the world of mathematical equations. Bu t whil e mathematicians , physicists , an d computer s hav e n o problem solvin g equations i n multidimensiona l space , human s fin d i t impossible to visualize universes beyond thei r own.

Worlds Beyond Space an d Time 1

1

At best, we can use a variety of mathematical tricks , devised by mathematician an d mysti c Charles Hinton a t the tur n o f the century, to visualize shadows of higher-dimensional objects . Other mathematicians, like Thomas Banchoff , chairman o f the mathematic s departmen t a t Brown University, have written computer programs tha t allow us to manipulat e higher-dimensional object s by projecting thei r shadow s ont o flat , twodimensional compute r screens . Like the Gree k philosopher Plato, who said that we are like cave dwellers condemned t o see only the dim , gray shadows of th e ric h lif e outsid e ou r caves , Banchoff s computers allow only a glimpse of the shadow s of higher-dimensional objects. (Actually, we cannot visualize higher dimension s because o f an acciden t of evolution. Ou r brain s hav e evolve d t o handl e myria d emergencies i n thre e dimensions. Instantly , without stopping t o think, we can recognize an d react t o a leapin g lio n o r a chargin g elephant . I n fact , thos e human s who coul d bette r visualiz e ho w object s move, turn , an d twis t i n thre e dimensions had a distinct survival advantage ove r those who could not . Unfortunately, ther e wa s no selectio n pressur e place d o n human s t o master motio n i n fou r spatia l dimensions. Being able t o see the fourth spatial dimensio n certainl y did no t hel p someon e fen d of f a chargin g saber-toothed tiger . Lion s an d tiger s d o no t lung e a t u s throug h th e fourth dimension. ) The Law s of Natur e Are Simple r in Highe r Dimension s One physicis t who delights in teasing audiences about the properties of higher-dimensional universes is Peter Freund, a professor of theoretical physics at the Universit y of Chicago's renowned Enrico Fermi Institute. Freund wa s one o f the earl y pioneers workin g on hyperspac e theorie s when it was considered to o outlandish fo r mainstream physics. For years, Freund an d a small group o f scientists dabbled in the science of higher dimensions in isolation; now, however, it has finally become fashionable and a legitimate branch o f scientific research . To his delight, he is finding tha t his early interest is at last paying off. Freund doe s not fit the traditiona l imag e of a narrow, crusty, disheveled scientist . Instead, h e is urbane, articulate , an d cultured , an d ha s a sly, impis h gri n tha t captivate s nonscientist s with fascinating stories o f fast-breaking scientifi c discoveries . He i s equally at ease scribbling on a blackboard littere d with dense equations o r exchanging light banter a t a cocktail party. Speaking with a thick, distinguished Romanian accent, Freund ha s a rar e knac k for explainin g th e mos t arcane , convolute d concepts o f physics in a lively, engaging style .

!2 E N T E R I N G T H E F I F T H D I M E N S I O

N

Traditionally, Freun d remind s us , scientist s hav e viewe d highe r dimensions with skepticism because they could not be measured and did not hav e an y particula r use . However , th e growin g realizatio n amon g scientists toda y i s tha t an y three-dimensiona l theor y i s "to o small " t o describe th e force s that govern ou r universe . As Freund emphasizes, one fundamental theme running through th e past decade o f physic s ha s bee n tha t th e laws o f nature become simpler an d elegant when expressed i n higher dimensions, whic h i s thei r natura l home . The law s of light and gravit y fin d a natural expressio n when expressed in higher-dimensiona l space-time. The ke y step in unifyin g th e law s of nature is to increase the number o f dimensions of space-time unti l more and mor e force s can be accommodated . I n higher dimensions , we have enough "room " to unif y al l known physical forces. Freund, in explaining why higher dimension s are exciting the imagination o f the scientifi c world, uses the followin g analogy: "Think, for a moment, o f a cheetah , a sleek, beautiful animal, on e o f th e fastes t o n earth, which roams freely on the savannas of Africa. I n its natural habitat, it is a magnificent animal, almost a work of art, unsurpassed i n speed o r grace by any other animal . Now," h e continues , think o f a cheeta h tha t ha s been capture d an d throw n int o a miserabl e cage in a zoo. It has lost its original grace and beauty , and i s put o n display for ou r amusement . We see onl y th e broke n spiri t o f the cheeta h i n th e cage, not it s original power and elegance . The cheeta h can be compared to th e law s o f physics , whic h ar c beautifu l i n thei r natura l setting . Th e natural habita t o f th e law s o f physic s i s higher-dimensional space-time . However, we ca n onl y measure th e law s o f physics when the y hav e bee n broken an d place d o n displa y i n a cage , whic h i s our three-dimensiona l laboratory. We only see the cheeta h when it s grace and beaut y have been stripped away. 2 For decades, physicist s have wondered wh y the fou r force s o f nature appear t o b e s o fragmented—wh y th e "cheetah " look s so pitifu l an d broken i n his cage. The fundamental reason wh y these four forces seem so dissimilar, notes Freund , i s that we have been observin g the "cage d cheetah." Ou r three-dimensiona l laboratorie s ar e steril e zoo cages for the law s o f physics . Bu t whe n w e formulate th e law s i n higher-dimen sional space-time, their natural habitat, we see their tru e brillianc e and power; the laws become simple and powerful. The revolutio n now sweeping over physics is the realizatio n that th e natura l hom e for the cheeta h may be hyperspace.

Worlds Beyond Space an d Time 1

3

To illustrat e how adding a higher dimensio n ca n mak e thing s simpler, imagin e ho w major wars were fought b y ancient Rome. The grea t Roman wars , ofte n involvin g many smaller battlefields , were invariably fought wit h great confusion, wit h rumors and misinformatio n pourin g in o n bot h side s from man y different directions. With battles raging on several fronts , Roman general s wer e often operatin g blind . Rom e won its battles more from brute strengt h tha n fro m the eleganc e o f its strategies. Tha t i s why one o f th e firs t principle s o f warfare is to seiz e th e high ground—tha t is, to go u p into the thir d dimension , above the twodimensional battlefield . From th e vantag e poin t o f a larg e hil l wit h a panoramic vie w o f th e battlefield , the chao s o f war suddenly become s vastly reduced. I n othe r words , viewed from th e thir d dimensio n (tha t is, fro m th e to p o f th e hill) , th e confusio n o f th e smalle r battlefields becomes integrate d int o a coherent singl e picture . Another applicatio n o f this principle—that nature become s simple r when expresse d i n highe r dimensions—i s the centra l ide a behin d Ein stein's special theory of relativity. Einstein revealed time to be the fourth dimension, and h e showe d tha t spac e an d tim e coul d convenientl y be unified i n a four-dimensional theory. This, in turn, inevitabl y led t o th e unification o f all physical quantities measure d b y space an d time , such as matter an d energy . He the n foun d th e precis e mathematica l expres sion for this unity between matter and energy : E = m