Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Read online

  HIDING IN THE MIRROR

  A L S O B Y L A W R E N C E M . K R A U S S Atom: A Single Oxygen Atom’s Journey from the Big Bang to Life on Earth . . . and Beyond

  Quintessence: The Mystery of the Missing Mass

  Beyond Star Trek: From Alien Invasions to the End of Time The Physics of Star Trek

  Fear of Physics: A Guide for the Perplexed

  The Fifth Essence: The Search for Dark Matter in the Universe G

  HIDING IN THE MIRROR T H E M Y S T E R I O U S A L L U R E O F E X T R A D I M E N S I O N S ,

  F R O M P L AT O T O S T R I N G T H E O R Y A N D B E Y O N D

  Lawrence M. Krauss

  V I K I N G

  VIKING

  Published by the Penguin Group

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  80 Strand, London WC2R 0RL, England First published in 2005 by Viking Penguin, a member of Penguin Group (USA) Inc.

  Copyright © Lawrence M. Krauss, 2009

  All rights reserved

  Figure on page 67: Brendan Crill, The Boomerang Collaboration. All other drawings by the author.

  ISBN: 1-4362-9493-2

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  For my mother . . . at last!

  There is a dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man’s fears and the summit of his knowledge. This is the dimension of imagination.

  —Rod Serling, The Twilight Zone

  R E M I N I S C E N C E

  A DIMENSIONAL LOVE AFFAIR

  Two parents wake in the middle of the night to sounds of their daughter’s crying out in the distance. The father rushes to her bedroom and finds her missing. He frantically searches everywhere, slowly com- ing to the grim realization that she is gone. His wife runs into the room soon afterward, overcome with panic. At his wit’s end, he dashes out to the living room and picks up the phone and calls a neighbor. He re- turns to his wife and, in words that are probably unique in the history of television, tells her:

  “Bill’s coming over. He’s a physicist! He ought to be able to help!”

  Forty-two years ago, when I was very young, a Twilight Zone episode called “Little Lost Girl” scared the living daylights out of me. Touching on every child’s fear of being separated from the safety of parents and home, the episode told the story of a little girl who falls into another dimension.

  When I first thought about writing a book that might focus on our love affair with extra dimensions, “Little Lost Girl” came immediately to mind, although I confess I had no memory of the episode’s title or when it aired. After a short bit of research on the Web, I was able to locate it, and a few days later, along with forty-two other episodes I had to buy in a Twi- light Zone boxed set, it arrived at my door.

  That night I placed the DVD into my computer and relived my childhood trauma. The eerie thing was that I remembered everything about the episode . . . except for the physicist! But suddenly, upon hearing that line of dialogue, a rush of memories came flooding back. Of course! The physicist was the hero of the episode. He came over in the middle of the night, discovered and traced out the “portal” in the wall through which the small child and her dog had wandered, guided her father through the gap, and ultimately reached through and saved the father and the terrified duo moments before this door to another dimension closed forever.

  I now vividly remember (or I think I remember) being struck by how exotic and powerful Bill the physicist’s knowledge seemed, and how much respect this knowledge engendered in his frightened neighbor. I, too, wanted one day to be privy to such secrets, and to explain them. I wanted to be the one whom people in distress knew they could count on. In short, the physicist-superhero!

  Alas, I have been a physicist for over twenty years now, and except for some students every now and then the night before an exam, no one has sought out my physics expertise when in distress. Nevertheless, I sometimes wonder if I write books such as this to fulfill my desire to provide what Bill had offered his neighbors: insights that physics has revealed about universal human mysteries, such as from whence we came, and what may lie beyond the darkness of the night. Some people seek solace through the spirit, but for others it comes through knowledge. As Rod Serling, the creator of the Twilight Zone, observed in his weekly introductions beginning in 1959, the human imagination can create whole universes into which we can travel via the depths of despair or the peaks of ecstasy. Ultimately our continuing intellectual fascination with extra dimensions may tell us more about our own human nature than it does about the universe itself.

  We all yearn to discover new realities hidden just out of sight. So much so, that we have continually reinvented them throughout human history, whenever the world of our experience has seemed lacking. But this does not necessarily mean that all of these worlds beyond our direct experience are unreal. There are scientists today who truly expect to discover the existence of extra dimensions and perhaps even extra universes in our lifetime. I originally began this book because I wanted to explore the unique cultural and scientific legacy that has led to our current fascination with exotic new realms that may lie hidden in the mirror. But I never guessed that the voyage could be so personal. I now realize that with seven words heard in a television program some forty-two years ago, my own future may have been determined.

  C H A P T E R 1

  THE PRIVILEGE TO LIVE IN SPACE?

  I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.

  So begins perhaps the most famous mathematical romance ever written. Penned in 1884, twenty-one years before Albert Einstein revolutionized our notions of space and time, under the pseudonym “A. Square” by the clergyman and Shakespearean scholar Edwin A. Abbott, Flatland was a poignant tale told by a wistful two-dimensional being who had just discovered the miraculous existence of three-dimensional space and longed to enjoy it. The unhappy hero of this saga urged us lucky Spacelanders to recognize the beauty of the higher-
dimensional universes that he thus envisaged.

  At around the same time that Abbott was writing Flatland, a lonely and tragic artist on the Continent was imagining another universe beyond the realm of our perception. Vincent Van Gogh was a tortured genius who is said to have sold but a single painting in his lifetime. Yet you cannot walk the streets of Amsterdam today without seeing reproductions in storefront windows of his haunting self-portraits or his landscapes with yellow skies and blue earth. In 1882, he wrote to his brother, who was his sole supporter, “I know for certain that I have a feeling for color, and shall acquire more and more.” Through his paintings Van Gogh freed our minds from the “tyranny” of color, daring us to imagine everyday objects in a completely different way, and thereby demonstrating that exotic realities could be discovered in even the otherwise most ordinary things. His paintings are haunting not because they are so bizarre but because they are just bizarre enough to capture the essence of reality while at the same time forcing us to reexamine what exactly reality is. These are the luxuries of art and literature: to create imaginary worlds that cause us to reconsider our place within our own world. Science has comparable impact. It, too, unveils different sorts of hidden worlds, but ones that we hope might also actually exist and, most importantly, can be measured. Nevertheless, the net result is the same: In the end we gain new insights into our own standing in the universe.

  All of these creative human activities reflect the essence of human imagination, the spark that raises our existence from the mundane to the extraordinary. If we couldn’t imagine the world as it might be, it is possible that the world of our experience would become intolerable. Such imagination almost defines what it means to be human. Fourteen thousand years ago, in what is now France, a remote Ice Age ancestor took a walk with a young child into what many of us today would think of as a dark and forbidding place. Deep in an underground cave the adult held the child’s hand against a wall and blew pigment over it, leaving a shadowlike imprint of a tiny hand that remains to this very day. We will never know the purpose of this adventure. Did it have some deep spiritual significance, or was it simply play? It certainly was not an everyday activity, as our Cro-Magnon ancestors did not tend to live in the deep recesses of caves such as this. Whatever its purpose, it represents something very special about humans that clearly differentiates us from our closest relatives on the evolutionary tree.

  I am not speaking here about art per se. Rather, I am addressing the deeper, symbolic sense of self that art reflects. The notion that the imprint on a wall might permanently record the presence of two individuals in the cave that day implies not only a recognition of their own existence, but also their desire to preserve some aspect of it against the vicissitudes of a dangerous world. For with a sense of self comes a sense of everything that isn’t self, or the “unknown possibilities of existence,” as the godlike alien Q on Star Trek once described it.

  That even earlier humans pondered such unknown possibilities is testified to by the existence of artistic renderings that predate the French cave art by at least eighteen thousand years. In a cave at a site called Hohlenstein-Stadel, in what is now Germany, a foot-tall figure of a standing human was discovered. No less striking than the skill of the artist who created it is the subject matter: This figure has the head of a lion, not a man. Did this early carving represent some primal notion of a deity? Or did it merely represent the recognition that if lions existed, and humans existed, then somewhere, some exotic combination of the two might exist?

  Of course, here again we shall probably never know what motivated our ancestral carver, but whatever its purpose the figure reflects an artistic imagining of the possibilities inherent either in this world or in one beyond it. In the three hundred centuries that have passed since this figure was created, human civilization, and human imagination, have evolved considerably. But there remains a fundamental connection between our modern efforts and these first, tentative steps: When we imagine the world beyond our experience, we are digging deep into our own psyches. In the famous Twilight Zone quote with which I began this book, Rod Serling argued that imagination is the middle ground between science and superstition. With that in mind, the central question becomes: To what extent do our imaginings reflect our own predilections, and to what extent might they actually mirror reality?

  If we can directly test our imaginings against the weight of observation and experiment, then the answer is easy. But what if we cannot? When certain notions persist, in many cultures and many times, are they merely hardwired in our brains? Or perhaps, even if they are, is it because we are the products of a natural world that incorporates them?

  One such notion will be the focus of this book: the longstanding love affair of the human intellect with the idea that there is far more “out there” than meets the eye. Science has, of course, validated this notion. Whole new realms of the physical world have been exposed by the spectacular scientific developments of the nineteenth and twentieth centuries. But in the present context I mean something more literally “out there.”

  Could space itself extend beyond the bounds of our experience, and can there be whole new dimensions of space just out of reach of our senses?

  It is difficult to disagree with Serling that imagination adds an extra dimension to the human experience. Still, the question remains: Is a fifth—or even an eleventh, or twenty-sixth—dimension purely imaginary?

  What if extra dimensions exist but they remain hidden from even the most sophisticated detectors? Can our imaginations alone enable us to pierce nature’s veil to discover them?

  This very question drove the most famous of all philosophers in Western history to write a tale about a two-dimensional world as an allegory for our own limited understanding of reality. Twenty-five hundred years ago, in his most famous set of Dialogues, The Republic, Plato invented the allegory of a cave to describe his belief in the possibility of uncovering hidden realities within all of the objects of our experience.

  Plato envisaged our lives as being like those of individuals confined in shackles within a cave, unable to directly see the world of light beyond. These prisoners viewed all objects located outside the mouth of the cave via the shadows they cast on the cave’s back wall. To the viewers, who had no other experience, the shadows themselves represented the real objects. Imagine, says Plato, through his interlocutor, Socrates, what it would be like to be unchained and dragged out to the light outside. First, of course, the brilliant glare would be painful, and one would crave a return to the dark familiarity of the cave. Ultimately, however, the true wonder of the world would become intoxicating—so much so that a return to one’s previous state of ignorant slavery would be unthinkable. And even if one did return, how would it be possible to communicate the truth without appearing mad to those who had no idea of it?

  Plato argued, however, that this is precisely the responsibility of a true philosopher. He must be willing to forsake the comfort of his own safe vision of reality and embark on travels through frightening new terrains of the mind. But more important, he must not be content to remain in his ivory tower of learning, separate from the rest of the human race, but must be willing to return to the world of men, to attempt to educate those who govern the affairs of men in the true workings of the universe. When Socrates was asked, in Plato’s dialogue, how one could penetrate the fog that shields us from the true workings of reality, his response was particularly telling, especially in light of our current scientific perspective. The answer involved the study of abstractions—in particular, arithmetic, the science of numbers. Or, as he put it, “Numbers, then, appear to lead towards the truth.”

  The study of numbers, said Socrates, should be followed by, in successively lesser importance, the study of geometry, then astronomy—as far as it concerns the laws of motion—then perhaps harmony, the study of sound. Only through the study of abstractions of the mind—as he viewed these disciplines—could one release oneself from the chains that bind us all to the rigid wo
rld of our senses.

  Plato’s entreaties now appear hauntingly modern. If his own abstraction—via the two-dimensional shadows of three-dimensional objects—might open the minds of his contemporaries to the infinite possibilities of existence, what mysteries might modern mathematical excursions unveil? Perhaps this spirit supplemented Abbott’s desire to create a piece of social satire when he penned Flatland.

  Indeed, the twentieth-century British mathematician and philosopher Bertrand Russell, in his Study of Mathematics, echoed almost verbatim Plato’s idealism about the hidden power of mathematics: Mathematics, rightly viewed, possesses not only truth, but supreme beauty . . . a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

  More recently we have become so accustomed to the superb predictive power of our mathematical descriptions of reality that it is easy to take this unexpected connection between human abstraction and the actual workings of the natural world for granted. Yet the mathematical physicist and Nobel laureate Eugene Wigner wrote a famous essay in 1960 entitled

  “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

  In it he mused about the remarkable success of mathematics as a description of natural phenomena, or, as he put it, “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and . . . there is no rational explanation for it.”

  It was precisely this latter fact—that the profound connection between mathematics and the natural world seems to be “a wonderful gift which we neither understand nor deserve,” as Wigner put it—that led him to speculate further. Does the “uncanny usefulness of mathematical concepts” suggest that a perhaps wholly different mathematics from that we have exploited to describe nature might perform equally well? Namely, are our physical theories unique—do they represent some fundamental underlying reality about nature—or have we just chosen one of many different, possibly equally viable, mathematical frameworks within which to pose our questions? In this latter case, would the apparent underlying physical pictures corresponding to these other mathematical descriptions each be totally different?