Hyperspace (3 page)

When finally constructed, the 300-pound, 6-kilowatt betatron consumed every ounce of energy my house produced. When I turned it on, I would usually blow every fuse, and the house would suddenly became dark. With the house plunged periodically into darkness, my mother would often shake her head. (I imagined that she probably wondered why she couldn’t have a child who played baseball or basketball, instead of building these huge electrical machines in the garage.) I was gratified that the machine successfully produced a magnetic field 20,000 times more powerful than the earth’s magnetic field, which is necessary to accelerate a beam of electrons.

Because my family was poor, my parents were concerned that I wouldn’t be able to continue my experiments and my education. Fortunately, the awards that I won for my various science projects caught the attention of the atomic scientist Edward Teller. His wife generously arranged for me to receive a 4-year scholarship to Harvard, allowing me to fulfill my dream.

Ironically, although at Harvard I began my formal training in theoretical physics, it was also where my interest in higher dimensions gradually died out. Like other physicists, I began a rigorous and thorough program of studying the higher mathematics of each of the forces of nature separately, in complete isolation from one another. I still remember solving a problem in electrodynamics for my instructor, and then asking him what the solution might look like if space were curved in a higher dimension. He looked at me in a strange way, as if I were a bit cracked. Like others before me, I soon learned to put aside my 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 to physics, and my thoughts would often drift back to the the carp living in the Tea Garden. Although the equations we used for electricity and magnetism, discovered by Maxwell in the nineteenth century, worked surprisingly well, the equations seemed rather arbitrary. I felt that physicists (like the carp) invented these “forces” to hide our ignorance of how objects can move each other without touching.

In my studies, I learned that one of the great debates of the nineteenth century had been about how light travels through a vacuum. (Light from the stars, in fact, can effortlessly travel trillions upon trillions of miles through the vacuum of outer space.) Experiments also showed beyond question that light is a wave. But if light were a wave, then it would require something to be “waving.” Sound waves require air, water waves require water, but since there is nothing to wave in a vacuum, we have a paradox. How can light be a wave if there is nothing to wave? So physicists conjured up a substance called the aether, which filled the vacuum and acted as the medium for light. However, experiments conclusively showed that the “aether” does not exist.
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Finally, when I became a graduate student in physics at the University of California at Berkeley, I learned quite by accident that there was an alternative, albeit controversial, explanation of how light can travel through a vacuum. This alternative theory was so outlandish that I received quite a jolt when I stumbled across it. That shock was similar to the one experienced by many Americans when they first heard that President John Kennedy had been shot. They can invariably remember the precise moment when they heard the shocking news, what they were doing, and to whom they were talking at that instant. We physicists, too, receive quite a shock when we first stumble across Kaluza-Klein theory for the first time. Since the theory was considered to be a wild speculation, it was never taught in graduate school; so young physicists are left to discover it quite by accident in their casual readings.

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 through a vacuum, it was because the vacuum itself was vibrating, because the “vacuum” really existed in four dimensions of space and one of time. By adding the fifth dimension, the force of gravity and light could be unified in a startlingly simple way. Looking back at my childhood experiences at the Tea Garden, I suddenly realized that this was the mathematical theory for which I had been looking.

The old Kaluza-Klein theory, however, had many difficult, technical problems that rendered it useless for over half a century. All this, however, has changed in the past decade. More advanced versions of the theory, like supergravity theory and especially superstring theory, have
finally eliminated the inconsistencies of the theory. Rather abruptly, the theory of higher dimensions is now being championed in research laboratories around the globe. Many of the world’s leading physicists now believe that dimensions beyond the usual four of space and time might exist. This idea, in fact, has become the focal point of intense scientific investigation. Indeed, many theoretical physicists now believe that higher dimensions may be the decisive step in creating a comprehensive theory that unites the laws of nature—a theory of hyperspace.

If it proves to be correct, then future historians of 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 secrets of nature and Creation itself.

This seminal concept has sparked an avalanche of scientific research: Several thousand papers written by theoretical physicists in the major research laboratories around the world have been devoted to exploring the properties of hyperspace. The pages of
Nuclear Physics
and
Physics Letters
, two leading scientific journals, have been flooded with articles analyzing the theory. More than 200 international physics conferences have been sponsored to explore the consequences of higher dimensions.

Unfortunately, we are still far from experimentally verifying that our universe exists in higher dimensions. (Precisely what it would take to prove the correctness of the theory and possibly harness the power of hyperspace will be discussed later in this book.) However, this theory has now become firmly established as a legitimate branch of modern theoretical physics. The Institute for Advanced Study at Princeton, for example, where Einstein spent the last decades of his life (and where this book was written), is now one of the active centers of research on higher-dimensional space-time.

Steven Weinberg, who won the Nobel Prize in physics in 1979, summarized this conceptual revolution when he commented recently that theoretical physics seems to be becoming more and more like science fiction.

These revolutionary ideas seem strange at first because we take for granted that our everyday world has three dimensions. As the late physicist Heinz Pagels noted, “One feature of our physical world is so obvious that most people are not even puzzled by it—the fact that space is three-dimensional.”
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Almost by instinct alone, we know that any object can be
described by giving its height, width, and depth. By giving three numbers, we can locate any position in space. If we want to meet someone for lunch in New York, we say, “Meet me on the twenty-fourth floor of the building at the corner of Forty-second Street and First Avenue.” Two numbers provide us the street corner; and the third, the height off the ground.

Airplane pilots, too, know exactly where they are with three numbers—their altitude and two coordinates that locate their position on a grid or map. In fact, specifying these three numbers can pinpoint any location in our world, from the tip of our nose to the ends of the visible universe. Even babies understand this: Tests with infants have shown that they will crawl to the edge of a cliff, peer over the edge, and crawl back. In addition to understanding “left” and “right” and “forward” and “backward” instinctively, babies instinctively understand “up” and “down.” Thus the intuitive concept of three dimensions is firmly embedded in our brains from an early age.

Einstein extended this concept to include time as the fourth dimension. For example, to meet that someone for lunch, we must specify that we should meet at, say, 12:30 P.M. in Manhattan; that is, to specify an event, we also need to describe its fourth dimension, the
time
at which the event takes place.

Scientists today are interested in going beyond Einstein’s conception of the fourth dimension. Current scientific interest centers on the fifth dimension (the spatial dimension beyond time and the three dimensions of space) and beyond. (To avoid confusion, throughout this book I have bowed to custom and called the fourth dimension the
spatial
dimension beyond length, breadth, and width. Physicists actually refer to this as the fifth dimension, but I will follow historical precedent. We will call time the fourth
temporal
dimension.)

How do we see the fourth spatial dimension?

The problem is, we can’t. Higher-dimensional spaces are impossible to visualize; so it is futile even to try. The prominent German physicist Hermann von Helmholtz compared the inability to “see” the fourth dimension with the inability of a blind man to conceive of the concept of color. No matter how eloquently we describe “red” to a blind person, words fail to impart the meaning of anything as rich in meaning as color. Even experienced mathematicians and theoretical physicists who have worked with higher-dimensional spaces for years admit that they cannot visualize them. Instead, they retreat into the world of mathematical equations. But while mathematicians, physicists, and computers have no problem solving equations in multidimensional space, humans find it impossible to visualize universes beyond their own.

At best, we can use a variety of mathematical tricks, devised by mathematician and mystic Charles Hinton at the turn of the century, to visualize shadows of higher-dimensional objects. Other mathematicians, like Thomas Banchoff, chairman of the mathematics department at Brown University, have written computer programs that allow us to manipulate higher-dimensional objects by projecting their shadows onto flat, two-dimensional computer screens. Like the Greek philosopher Plato, who said that we are like cave dwellers condemned to see only the dim, gray shadows of the rich life outside our caves, Banchoff s computers allow only a glimpse of the shadows of higher-dimensional objects. (Actually, we cannot visualize higher dimensions because of an accident of evolution. Our brains have evolved to handle myriad emergencies in three dimensions. Instantly, without stopping to think, we can recognize and react to a leaping lion or a charging elephant. In fact, those humans who could better visualize how objects move, turn, and twist in three dimensions had a distinct survival advantage over those who could not. Unfortunately, there was no selection pressure placed on humans to master motion in four spatial dimensions. Being able to see the fourth spatial dimension certainly did not help someone fend off a charging saber-toothed tiger. Lions and tigers do not lunge at us through the fourth dimension.)

One physicist who delights in teasing audiences about the properties of higher-dimensional universes is Peter Freund, a professor of theoretical physics at the University of Chicago’s renowned Enrico Fermi Institute. Freund was one of the early pioneers working on hyperspace theories when it was considered too outlandish for mainstream physics. For years, Freund and a small group of scientists dabbled in the science of higher dimensions in isolation; now, however, it has finally become fashionable and a legitimate branch of scientific research. To his delight, he is finding that his early interest is at last paying off.

Freund does not fit the traditional image of a narrow, crusty, disheveled scientist. Instead, he is urbane, articulate, and cultured, and has a sly, impish grin that captivates nonscientists with fascinating stories of fast-breaking scientific discoveries. He is equally at ease scribbling on a blackboard littered with dense equations or exchanging light banter at a cocktail party. Speaking with a thick, distinguished Romanian accent, Freund has a rare knack for explaining the most arcane, convoluted concepts of physics in a lively, engaging style.

Traditionally, Freund reminds us, scientists have viewed higher dimensions with skepticism because they could not be measured and did not have any particular use. However, the growing realization among scientists today is that any three-dimensional theory is “too small” to describe the forces that govern our universe.

As Freund emphasizes, one fundamental theme running through the past decade of physics has been that
the laws of nature become simpler and elegant when expressed in higher dimensions
, which is their natural home. The laws of light and gravity find a natural expression when expressed in higher-dimensional space-time. The key step in unifying the laws of nature is to increase the number of dimensions of space-time until more and more forces can be accommodated. In higher dimensions, we have enough “room” to unify all known physical forces.

Freund, in explaining why higher dimensions are exciting the imagination of the scientific world, uses the following analogy: “Think, for a moment, of a cheetah, a sleek, beautiful animal, one of the fastest on earth, which roams 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 other animal. Now,” he continues,

think of a cheetah that has been captured and thrown into a miserable cage in a zoo. It has lost its original grace and beauty, and is put on display for our amusement. We see only the broken spirit of the cheetah in the cage, not its original power and elegance. The cheetah can be compared to the laws of physics, which are beautiful in their natural setting. The natural habitat of the laws of physics is higher-dimensional space-time. However, we can only measure the laws of physics when they have been broken and placed on display in a cage, which is our three-dimensional laboratory. We only see the cheetah when its grace and beauty have been stripped away.
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