Hyperspace (5 page)

Wormholes can be visualized with a sheet of paper and a pair of scissors: Take a piece of paper, cut two holes in it, and then reconnect the two holes with a long tube (
Figure 1.1
). As long as you avoid walking into the wormhole, our world seems perfectly normal. The usual laws of geometry taught in school are obeyed. However, if you fall into the wormhole, you are instantly transported to a different region of space and time. Only by retracing your steps and falling back into the worm-hole can you return to your familiar world.

Although wormholes provide a fascinating area of research, perhaps the most intriguing concept to emerge from this discussion of hyperspace is the question of time travel. In the film
Back to the Future
, Michael J. Fox journeys back in time and meets his parents as teenagers before they were married. Unfortunately, his mother falls in love with
him
and spurns his father, raising the ticklish question of how he will be born if his parents never marry and have children.

Figure 1.1. Parallel universes may be graphically represented by two parallel planes. Normally, they never interact with each other. However, at times worm-holes or tubes may open up between them, perhaps making communication and travel possible between them,. This is now the subject of intense interest among theoretical physicists
.

Traditionally, scientists have held a dim opinion of anyone who raised the question of time travel. Causality (the notion that every effect is preceded, not followed, by a cause) is firmly enshrined in the foundations
of modern science. However, in the physics of wormholes, “acausal” effects show up repeatedly. In fact, we have to make strong assumptions in order to prevent time travel from taking place. The main problem is that wormholes may connect not only two distant points in space, but also the future with the past.

In 1988, physicist Kip Thorne of the California Institute of Technology and his collaborators made the astonishing (and risky) claim that time travel is indeed not only possible, but probable under certain conditions. They published their claim not in an obscure “fringe” journal, but in the prestigious
Physical Review Letters
. This marked the first time that reputable physicists, and not crackpots, were scientifically advancing a claim about changing the course of time itself. Their announcement was based on the simple observation that a wormhole connects two regions that exist in different time periods. Thus the wormhole may connect the present to the past. Since travel through the wormhole is nearly instantaneous, one could use the wormhole to go backward in time. Unlike the machine portrayed in H. G. Wells’s
The Time Machine
, however, which could hurl the protagonist hundreds of thousands of years into England’s distant future with the simple twist of a dial, a worm-hole may require vast amounts of energy for its creation, beyond what will be technically possible for centuries to come.

Another bizarre consequence of wormhole physics is the creation of “baby universes” in the laboratory. We are, of course, unable to re-create the Big Bang and witness the birth of our universe. However, Alan Guth of the Massachusetts Institute of Technology, who has made many important contributions in cosmology, shocked many physicists a few years ago when he claimed that the physics of wormholes may make it possible to create a baby universe of our own in the laboratory. By concentrating intense heat and energy in a chamber, a wormhole may eventually open up, serving as an umbilical cord connecting our universe to another, much smaller universe. If possible, it would give a scientist an unprecedented view of a universe as it is created in the laboratory.

Some of these concepts are not new. For the past several centuries, mystics and philosophers have speculated about the existence of other universes and tunnels between them. They have long been fascinated by the possible existence of other worlds, undetectable by sight or sound, yet coexisting with our universe. They have been intrigued by the possibility
that these unexplored, nether worlds may even be tantalizingly close, in fact surrounding us and permeating us everywhere we move, yet just beyond our physical grasp and eluding our senses. Such idle talk, however, was ultimately useless because there was no practical way in which to mathematically express and eventually test these ideas.

Gateways between our universe and other dimensions are also a favorite literary device. Science-fiction writers find higher dimensions to be an indispensable tool, using them as a medium for interstellar travel. 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 other galaxies, rockets merely zip along in hyperspace by warping the space around them. For instance, in the film
Star Wars
, hyperspace is a refuge where Luke Skywalker can safely evade the Imperial Starships of the Empire. In the television series “Star Trek: Deep Space Nine,” a worm-hole opens up near a remote space station, making it possible to span enormous distances across the galaxy within seconds. The space station suddenly becomes the center of intense intergalactic rivalry over who should control such a vital link to other parts of the galaxy.

Ever since Flight 19, a group of U.S. military torpedo bombers, vanished in the Caribbean 30 years ago, mystery writers too have used higher dimensions as a convenient solution to the puzzle of the Bermuda Triangle, or Devil’s Triangle. Some have conjectured that airplanes and ships disappearing in the Bermuda Triangle actually entered some sort of passageway to another world.

The existence of these elusive parallel worlds has also produced endless religious speculation over the centuries. Spiritualists have wondered whether the souls of departed loved ones drifted into another dimension. The seventeenth-century British philosopher Henry More argued that ghosts and spirits did indeed exist and claimed that they inhabited the fourth dimension. In
Enchiridion Metaphysicum
(1671), he argued for the existence of a nether realm beyond our tangible senses that served as a home for ghosts and spirits.

Nineteenth-century theologians, at a loss to locate heaven and hell, pondered whether they might be found in a higher dimension. Some wrote about a universe consisting of three parallel planes: the earth, heaven, and hell. God himself, according to the theologian Arthur Willink, found his home in a world far removed from these three planes; he lived in infinite-dimensional space.

Interest in higher dimensions reached its peak between 1870 and 1920, when the “fourth dimension” (a spatial dimension, different from
what we know as the fourth dimension of time) seized the public imagination and gradually cross-fertilized every branch of the arts and sciences, becoming a metaphor for the strange and mysterious. The fourth dimension appeared in the literary works of Oscar Wilde, Fyodor Dostoyevsky, Marcel Proust, H. G. Wells, and Joseph Conrad; it inspired some of the musical works of Alexander Scriabin, Edgard Varèse, and George Antheil. It fascinated such diverse personalities as psychologist William James, literary figure Gertrude Stein, and revolutionary socialist Vladimir Lenin.

The fourth dimension also inspired the works of Pablo Picasso and Marcel Duchamp and heavily influenced the development of Cubism and Expressionism, two of the most influential art movements in this century. Art historian Linda Dalrymple Henderson writes, “Like a Black Hole, ‘the fourth dimension’ possessed mysterious qualities that could not be completely understood, even by the scientists themselves. Yet, the impact of ‘the fourth dimension’ was far more comprehensive than that of Black Holes or any other more recent scientific hypothesis except Relativity Theory after 1919.”
⁵

Similarly, mathematicians have long been intrigued by alternative forms of logic and bizarre geometries that defy every convention of common sense. For example, the mathematician Charles L. Dodgson, who taught at Oxford University, delighted generations of schoolchildren by writing books—as Lewis Carroll—that incorporate these strange mathematical ideas. When Alice falls down a rabbit hole or steps through the looking glass, she enters Wonderland, a strange place where Cheshire cats disappear (leaving only their smile), magic mushrooms turn children into giants, and Mad Hatters celebrate “unbirthdays.” The looking glass somehow connects Alice’s world with a strange land where everyone speaks in riddles and common sense isn’t so common.

Some of the inspiration for Lewis Carroll’s ideas most likely came from the great nineteenth-century German mathematician Georg Bernhard Riemann, who was the first to lay the mathematical foundation of geometries in higher-dimensional space. Riemann changed the course of mathematics for the next century by demonstrating that these universes, as strange as they may appear to the layperson, are completely self-consistent and obey their own inner logic. To illustrate some of these ideas, think of stacking many sheets of paper, one on top of another. Now imagine that each sheet represents an entire world and that each world obeys its own physical laws, different from those of all the other worlds. Our universe, then, would not be alone, but would be one of
many possible parallel worlds. Intelligent beings might inhabit some of these planes, completely unaware of the existence of the others. On one sheet of paper, we might have Alice’s bucolic English countryside. On another sheet might be a strange world populated by mythical creatures in the world of Wonderland.

Normally, life proceeds on each of these parallel planes independent of the others. On rare occasions, however, the planes may intersect and, for a brief moment, tear the fabric of space itself, which opens up a hole—or gateway—between these two universes. Like the wormhole appearing in “Star Trek: Deep Space Nine,” these gateways make travel possible between these worlds, like a cosmic bridge linking two different universes or two points in the same universe (
Figure 1.2
). Not surprisingly, Carroll found children much more open to these possibilities than adults, whose prejudices about space and logic become more rigid over time. In fact, Riemann’s theory of higher dimensions, as interpreted by Lewis Carroll, has become a permanent part of children’s literature and folklore, giving birth to other children’s classics over the decades, such as Dorothy’s Land of Oz and Peter Pan’s Never Never Land.

Without any experimental confirmation or compelling physical motivation, however, these theories of parallel worlds languished as a branch of science. Over 2 millennia, scientists have occasionally picked up the notion of higher dimensions, only to discard it as an untestable and therefore silly idea. Although Riemann’s theory of higher geometries was mathematically intriguing, it was dismissed as clever but useless. Scientists willing to risk their reputations on higher dimensions soon found themselves ridiculed by the scientific community. Higher-dimensional space became the last refuge for mystics, cranks, and charlatans.

In this book, we will study the work of these pioneering mystics, mainly because they devised ingenious ways in which a nonspecialist could “visualize” what higher-dimensional objects might look like. These tricks will prove useful to understand how these higher-dimensional theories may be grasped by the general public.

By studying the work of these early mystics, we also see more clearly what was missing from their research. We see that their speculations lacked two important concepts: a physical and a mathematical principle. From the perspective of modern physics, we now realize that the missing
physical
principle is that hyperspace simplifies the laws of nature, providing the possibility of unifying all the forces of nature by purely geometric arguments. The missing
mathematical
principle is called
field theory
, which is the universal mathematical language of theoretical physics.

Figure 1.2. Wormholes may connect a universe with itself, perhaps providing a means of interstellar travel. Since wormholes may connect two different time eras, they may also provide a means for time travel. Wormholes may also connect an infinite series of parallel universes. The hope is that the hyperspace theory will be able to determine whether wormholes are physically possible or merely a mathematical curiosity
.