The first book-length exploration of the most exciting development in modern physics, the theory of 10-dimensional space. The theory of hyperspace, which Michio Kaku pioneered, may be the leading candidate for the Theory of Everything that Einstein spent the remaining years of his life searching for.
HYPERSPACE A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension Michio Kaku Illustrations by Robert O'Keefe ANCHOR BOOKS DOUBLEDAY New York London Toronto Sydney Auckland AN ANCHOR BOOK PUBLISHED BY DOUBLEDAY a division of Bantam Doubleday Dell Publishing Group, Inc. 1540 Broadway, New York, New York 10036 ANCHOR BOOKS, DOUBLEDAY, and the portrayal of an anchor are trademarks of Doubleday, a division of Bantam Doubleday Dell Publishing Group, Inc. Hyperspace was originally published in hardcover by Oxford University Press in 1994. The Anchor Books edition is published by arrangement with Oxford University Press. "Cosmic Gall." From Telephone Poles and Other Poems by John Updike. Copyright © 1960 by John Updike. Reprinted by permission of Alfred A. Knopf, Inc. Originally appeared in The New Yorker. Excerpt from "Fire and Ice." From The Poetry of Robert Frost, edited by Edward Connery Lathem. Copyright 1951 by Robert Frost. Copyright 1923, © 1969 by Henry Holt and Company, Inc. Reprinted by permission of Henry Holt and Company, Inc. Library of Congress Cataloging-in-Publication Data Kaku, Michio. Hyperspace: a scientific odyssey through parallel universes, time warps, and the tenth dimension / Michio Kaku; illustrations by Robert O'Keefe. p. cm. Includes bibliographical references and index. 1. Physics. 2. Astrophysics. 3. Mathematical physics. I. Title. QC21.2.K3 1994 530.1'42—dc20 94-36657 CIP ISBN 0-385-47705-8 Copyright © 1994 by Oxford University Press All Rights Reserved Printed in the United States of America First Anchor Books Edition: March 1995 10 987654321 This book is dedicated to my parents Preface Scientific revolutions, almost by definition, defy common sense. If all our common-sense notions about the universe were correct, then science would have solved the secrets of the universe thousands of years ago. The purpose of science is to peel back the layer of the appear- ance of objects to reveal their underlying nature. In fact, if appearance and essence were the same thing, there would be no need for science. Perhaps the most deeply entrenched common-sense notion about our world is that it is three dimensional. It goes without saying that length, width, and breadth suffice to describe all objects in our visible universe. Experiments with babies and animals have shown that we are born with an innate sense that our world is three dimensional. If we include time as another dimension, then four dimensions are sufficient to record all events in the universe. No matter where our instruments have probed, from deep within the atom to the farthest reaches of the galactic cluster, we have only found evidence of these four dimensions. To claim otherwise publicly, that other dimensions might exist or that our universe may coexist with others, is to invite certain scorn. Yet this deeply ingrained prejudice about our world, first speculated on by ancient Greek philosophers 2 millennia ago, is about to succumb to the progress of science. This book is about a scientific revolution created by the theory of hyper- space, 1 which states that dimensions exist beyond the commonly accepted four of space and time. There is a growing acknowledgment among physicists worldwide, including several Nobel laureates, that the universe may actually exist in higher-dimensional space. If this theory is proved correct, it will create a profound conceptual and philosophical revolu- tion in our understanding of the universe. Scientifically, the hyperspace theory goes by the names of Kaluza-Klein theory and supergravity. But viii Preface its most advanced formulation is called superstring theory, which even predicts the precise number of dimensions: ten. The usual three dimen- sions of space (length, width, and breadth) and one of time are now extended by six more spatial dimensions. We caution that the theory of hyperspace has not yet been experi- mentally confirmed and would, in fact, be exceedingly difficult to prove in the laboratory. However, the theory has already swept across the major physics research laboratories of the world and has irrevocably altered the scientific landscape of modern physics, generating a staggering num- ber of research papers in the scientific literature (over 5,000 by one count). However, almost nothing has been written for the lay audience to explain the fascinating properties of higher-dimensional space. Therefore, the general public is only dimly aware, if at all, of this revo- lution. In fact, the glib references to other dimensions and parallel uni- verses in the popular culture are often misleading. This is regrettable because the theory's importance lies in its power to unify all known physical phenomena in an astonishingly simple framework. This book makes available, for the first time, a scientifically authoritative but acces- sible account of the current fascinating research on hyperspace. To explain why the hyperspace theory has generated so much excite- ment within the world of theoretical physics, I have developed four fun- damental themes that run through this book like a thread. These four themes divide the book into four parts. In Part I, I develop the early history of hyperspace, emphasizing the theme that the laws of nature become simpler and more elegant when expressed in higher dimensions. To understand how adding higher dimensions can simplify physical problems, consider the following example: To the ancient Egyptians, the weather was a complete mystery. What caused the seasons? Why did it get warmer as they traveled south? Why did the winds 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 rocket into outer space, where they can see the earth as simple and whole in its orbit around the sun. Suddenly, the answers to these ques- tions become obvious. From outer space, it is clear that the earth's axis is tilted about 23 degrees from the vertical (the 'vertical" being the perpendicular to the plane of the earth's orbit around the sun). Because of this tilt, the north- ern hemisphere receives much less sunlight during one part of its orbit than during another part. Hence we have winter and summer. And since Preface ix the equator receives more sunlight then the northern or southern polar regions, it becomes warmer as we approach the equator. Similarly, since the earth spins counterclockwise to someone sitting on the north pole, the cold, polar air swerves as it moves south toward the equator. The motion of hot and cold masses of air, set in motion by the earth's spin, thus helps to explain why the winds generally blow in one direction, depending on where you are on the earth. In summary, the rather obscure laws of the weather are easy to under- stand once we view the earth from space. Thus the solution to the prob- lem is to go up into space, into the third dimension. Facts that were impos- sible to understand in a flat world suddenly become obvious when viewing a three-dimensional earth. Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimen- sions of space and time, then the equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained as vibrations in the fifth dimension. In this way, we see that the laws of light and gravity become simpler in five dimen- sions. Consequently, many physicists are now convinced that a conventional four-dimensional theory is "too small" to describe adequately the forces that describe our universe. In a four-dimensional theory, physicists have to squeeze together the forces of nature in a clumsy, unnatural fashion. Furthermore, this hybrid theory is incorrect. When expressed in dimen- sions beyond four, however, we have "enough room" to explain the fundamental forces in an elegant, self-contained fashion. In Part II, we further elaborate on this simple idea, emphasizing that the hyperspace theory may be able to unify all known laws of nature into one theory. Thus the hyperspace theory may be the crowning achieve- ment of 2 millennia of scientific investigation: the unification of all known physical forces. It may give us the Holy Grail of physics, the "the- ory of everything" that eluded Einstein for so many decades. For the past half-century, scientists have been puzzled as to why the basic forces that hold together the cosmos—gravity, electromagnetism, and the strong and weak nuclear forces—differ so greatly. Attempts by the greatest minds of the twentieth century to provide a unifying picture of all the known forces have failed. However, the hyperspace theory allows the possibility of explaining the four forces of nature as well as the seemingly random collection of subatomic particles in a truly elegant X Preface fashion. In the hyperspace theory, "matter" can be also viewed as the vibrations that ripple through the fabric of space and time. Thus follows the fascinating possibility that everything we see around us, from the trees and mountains to the stars themselves, are nothing but vibrations in hyperspace. If this is true, then this gives us an elegant, simple, and geometric means of providing a coherent and compelling description of the entire universe. In Part III, we explore the possibility that, under extreme circum- stances, space may be stretched until it rips or tears. In other words, hyperspace may provide a means to tunnel through space and time. Although we stress that this is still highly speculative, physicists are seri- ously analyzing the properties of "wormholes," of tunnels that link dis- tant parts of space and time. Physicists at the California Institute of Tech- nology, for example, have seriously proposed the possibility of building a time machine, consisting of a wormhole that connects the past with the future. Time machines have now left the realm of speculation and fantasy and have become legitimate fields of scientific research. Cosmologists have even proposed the startling possibility that our universe is just one among an infinite number of parallel universes. These universes might be compared to a vast collection of soap bubbles suspended in air. Normally, contact between these bubble universes is impossible, but, by analyzing Einstein's equations, cosmologists have shown that there might exist a web of wormholes, or tubes, that connect these parallel universes. On each bubble, we can define our own dis- tinctive space and time, which have meaning only on its surface; outside these bubbles, space and time have no meaning. Although many consequences of this discussion are purely theoreti- cal, hyperspace travel may eventually provide the most practical appli- cation of all: to save intelligent life, including ours, from the death of the universe. Scientists universally believe that the universe must even- tually die, and with it all life that has evolved over billions of years. For example, according to the prevailing theory, called the Big Bang, a cos- mic explosion 15 to 20 billion years ago set the universe expanding, hurling stars and galaxies away from us at great velocities. However, if the universe one day stops expanding and begins to contract, it will eventually collapse into a fiery cataclysm called the Big Crunch, in which all intelligent life will be vaporized by fantastic heat. Nevertheless, some physicists have speculated that the hyperspace theory may provide the one and only hope of a refuge for intelligent life. In the last seconds of the death of our universe, intelligent life may escape the collapse by fleeing into hyperspace. Preface xi In Part IV, we conclude with a final, practical question: If the theory is proved correct, then when will we be able to harness the power of the hyperspace theory? This is not just an academic question, because in the past, the harnessing of just one of the four fundamental forces irrevo- cably changed the course of human history, lifting us from the ignorance and squalor of ancient, preindustrial societies to modern civilization. In some sense, even the vast sweep of human history can be viewed in a new light, in terms of the progressive mastery of each of the four forces. The history of civilization has undergone a profound change as each of these forces was discovered and mastered. For example, when Isaac Newton wrote down the classical laws of gravity, he developed the theory of mechanics, which gave us the laws governing machines. This, in turn, greatly accelerated the Industrial Rev- olution, which unleashed political forces that eventually overthrew the feudal dynasties of Europe. In the mid-1860s, when James Clerk Maxwell wrote down the fundamental laws of the electromagnetic force, he ush- ered in the Electric Age, which gave us the dynamo, radio, television, radar, household appliances, the telephone, microwaves, consumer elec- tronics, the electronic computer, lasers, and many other electronic mar- vels. Without the understanding and utilization of the electromagnetic force, civilization would have stagnated, frozen in a time before the dis- covery of the light bulb and the electric motor. In the mid-1940s, when the nuclear force was harnessed, the world was again turned upside down with the development of the atomic and hydrogen bombs, the most destructive weapons on the planet. Because we are not on the verge of a unified understanding of all the cosmic forces governing the uni- verse, one might expect that any civilization that masters the hyperspace theory will become lord of the universe. Since the hyperspace theory is a well-defined body of mathematical equations, we can calculate the precise energy necessary to twist space and time into a pretzel or to create wormholes linking distant parts of our universe. Unfortunately, the results are disappointing. The energy required far exceeds anything that our planet can muster. In fact, the energy is a quadrillion times larger than the energy of our largest atom smashers. We must wait centuries or even millennia until our civilization develops the technical capability of manipulating space-time, or hope for contact with an advanced civilization that has already mastered hyperspace. The book therefore ends by exploring the intriguing but speculative scientific question of what level of technology is necessary for us to become masters of hyperspace. Because the hyperspace theory takes us far beyond normal, common- xii Preface sense conceptions of space and time, I have scattered throughout the text a few purely hypothetical stories. I was inspired to utilize this ped- agogical technique by the story of Nobel Prize winner Isidore I. Rabi addressing an audience of physicists. He lamented the abysmal state of science education in the United States and scolded the physics com- munity for neglecting its duty in popularizing the adventure of science for the general public and especially for the young. In fact, he admon- ished, science-fiction writers had done more to communicate the romance of science than all physicists combined. In a previous book, Beyond Einstein: The Cosmic Quest for the Theory of the Universe (coauthored with Jennifer Trainer), I investigated super- string theory, described the nature of subatomic particles, and discussed at length the visible universe and how all the complexities of matter might be explained by tiny, vibrating strings. In this book, I have expanded on a different theme and explored the invisible universe—that is, the world of geometry and space-time. The focus of this book is not the nature of subatomic particles, but the higher-dimensional world in which they probably live. In the process, readers will see that higher-dimensional space, instead of being an empty, passive backdrop against which quarks play out their eternal roles, actually becomes the central actor in the drama of nature. In discussing the fascinating history of the hyperspace theory, we will see that the search for the ultimate nature of matter, begun by the Greeks 2 millennia ago, has been a long and tortuous one. When the final chapter in this long saga is written by future historians of science, they may well record that the crucial breakthrough was the defeat of common-sense theories of three or four dimensions and the victory of the theory of hyperspace. New York May 1993 M.K. Acknowledgments In writing this book, I have been fortunate to have Jeffrey Robbins as my editor. He was the editor who skillfully guided the progress of three of my previous textbooks in theoretical physics written for the scientific community, concerning the unified field theory, superstring theory, and quantum field theory. This book, however, marks the first popular sci- ence book aimed at a general audience that I have written for him. It has always been a rare privilege to work closely with him. I would also like to thank Jennifer Trainer, who has been my coau- thor on two previous popular books. Once again, she has applied her considerable skills to make the presentation as smooth and coherent as possible. I am also grateful to numerous other individuals who have helped to strengthen and criticize earlier drafts of this book: Burt Solomon, Leslie Meredith, Eugene Mallove, and my agent, Stuart Krichevsky. Finally, I would like to thank the Institute for Advanced Study at Princeton, where much of this book was written, for its hospitality. The Institute, where Einstein spent the last decades of his life, was an appro- priate place to write about the revolutionary developments that have extended and embellished much of his pioneering work. [...]... likely came from the great nineteenth-century G e r m a n mathematician Georg Bernh a r d Riemann, who was the first to lay the mathematical foundation of geometries in higher-dimensional space Riemann c h a n g e d the course of mathematics for the next century by demonstrating that these universes, as strange as they may a p p e a r to t h e layperson, are completely self-consistent a n d obey their... best, we can use a variety of mathematical tricks, devised by mathematician a n d mystic Charles H i n t o n at the turn of the century, to visualize shadows of higher-dimensional objects O t h e r mathematicians, like T h o m a s Banchoff, chairman of the mathematics d e p a r t m e n t at Brown University, have written c o m p u t e r programs that allow us to manipulate higher-dimensional objects... a n d fight certain forms of cancer T h e force of radioactive decay can also be deadly: It wreaked havoc at T h r e e Mile Island a n d Chernobyl; it also creates radioactive waste, the inevitable byp r o d u c t of nuclear weapons p r o d u c t i o n a n d commercial nuclear power plants, which may remain harmful for millions of years The Gravitational Force T h e gravitational force keeps the earth... the earth a n d the planets in their orbits a n d binds the galaxy Without the gravitational force of the earth, we Worlds Beyond Space and Time 15 would be flung into space like rag dolls by the spin of the earth T h e air we b r e a t h e would be quickly diffused into space, causing us to asphyxiate a n d making life on earth impossible Without the gravitational force of the sun, all the planets, including... e a r o u n d the planet to p l u m m e t Ironically, it is also the strong nuclear force that may o n e day take back the gift of life Unleashed in the hydrogen b o m b , the strong nuclear force could o n e day e n d all life on earth The Weak Nuclear Force T h e weak nuclear force governs certain forms of radioactive decay Because radioactive materials emit h e a t when they decay or break apart,... Because of the astronomical distances separating the stars in the heavens, science-fiction writers use higher dimensions as a clever shortcut between the stars Instead of taking the long, direct route to o t h e r galaxies, rockets merely zip along in hyperspace by warping the space a r o u n d them For instance, in the film Star Wars, hyperspace is a refuge where Luke Skywalker can safely evade the. .. freely on the savannas of Africa In its natural habitat, it is a magnificent animal, almost a work of art, unsurpassed in speed or grace by any o t h e r animal Now," he continues, think of a c h e e t a h that has b e e n captured a n d thrown i n t o a miserable c a g e i n a z o o I t has lost its o r i g i n a l g r a c e a n d b e a u t y , a n d i s p u t o n d i s p l a y f o r o u r a m u s e m... This alternative theory gave the simplest explanation of light: that it was really a vibration of the fifth dimension, or what used to called the fourth dimension by the mystics If light could travel t h r o u g h a vacuum, it was because t h e vacuum itself was vibrating, because t h e " v a c u u m " really existed in four dimensions of space a n d o n e of time By adding the fifth dimension, the. .. wormholes provide a fascinating area of research, p e r h a p s the most intriguing concept to emerge from this discussion of hyperspace Worlds Beyond Space and Time 19 Figure 1.1 Parallel universes may be graphically represented by two parallel planes Normally, they never interact with each other However, at times wormholes or tubes may open up between them, perhaps making communication and travel possible... as a practical model of o u r universe These models are the scientific analogue of Alice's looking glass W h e n Lewis Carroll's White Rabbit falls down the rabbit hole to e n t e r Wonderland, he actually falls down a wormhole Wormholes can be visualized with a sheet of p a p e r a n d a pair of scissors: Take a piece of paper, cut two holes in it, a n d then r e c o n n e c t the two holes with a . Cataloging-in-Publication Data Kaku, Michio. Hyperspace: a scientific odyssey through parallel universes, time warps, and the tenth dimension / Michio Kaku; . built a 2.3-million-electron-volt betatron in my garage that would be pow- erful enough to produce a beam of antielectrons. To construct the mon- strous