Hyperspace (6 page)

Fields were first introduced by the great nineteenth-century British scientist Michael Faraday. The son of a poor blacksmith, Faraday was a self-taught genius who conducted elaborate experiments on electricity and magnetism. He visualized “lines of force” that, like long vines spreading from a plant, emanated from magnets and electric charges in all directions and filled up all of space. With his instruments, Faraday could measure the strength of these lines of force from a magnetic or an electric charge at any point in his laboratory. Thus he could assign a series of numbers (the strength and direction of the force) to that point (and any point in space). He christened the totality of these numbers at any point in space, treated as a single entity, a field. (There is a famous story concerning Michael Faraday. Because his fame had spread far and wide, he was often visited by curious bystanders. When one asked what his work was good for, he answered, “What is the use of a child? It grows to be a man.” One day, William Gladstone, then Chancellor of the Exchequer, visited Faraday in his laboratory. Knowing nothing about science, Gladstone sarcastically asked Faraday what use the huge electrical contraptions in his laboratory could possibly have for England. Faraday replied, “Sir, I know not what these machines will be used for, but I am sure that one day you will tax them.” Today, a large portion of the total wealth of England is invested in the fruit of Faraday’s labors.)

Simply put, a
field
is a collection of numbers defined at every point in space that completely describes a force at that point. For example, three numbers at each point in space can describe the intensity and direction of the magnetic lines of force. Another three numbers everywhere in space can describe the electric field. Faraday got this concept when he thought of a “field” plowed by a farmer. A farmer’s field occupies a two-dimensional region of space. At each point in the farmer’s field, one can assign a series of numbers (which describe, for example, how many seeds there are at that point). Faraday’s field, however, occupies a three-dimensional region of space. At each point, there is a series of six numbers that describes both the magnetic and electric lines of force.

What makes Faraday’s field concept so powerful is that all forces of nature can be expressed as a field. However, we need one more ingredient before we can understand the nature of any force: We must be able to write down the equations that these fields obey. The progress of the past hundred years in theoretical physics can be succinctly summarized as the search for the
field equations
of the forces of nature.

For example, in the 1860s, Scottish physicist James Clerk Maxwell wrote down the field equations for electricity and magnetism. In 1915, Einstein discovered the field equations for gravity. After innumerable false starts, the field equations for the subatomic forces were finally written down in the 1970s, utilizing the earlier work of C. N. Yang and his student R. L. Mills. These fields, which govern the interaction of all subatomic particles, are now called
Yang-Mills fields
. However, the puzzle that has stumped physicists within this century is why the subatomic field equations look so vastly different from the field equations of Einstein—that is, why the nuclear force seems so different from gravity. Some of the greatest minds in physics have tackled this problem, only to fail.

Perhaps the reason for their failure is that they were trapped by common sense. Confined to three or four dimensions, the field equations of the subatomic world and gravitation are difficult to unify. The advantage of the hyperspace theory is that the Yang-Mills field, Maxwell’s field, and Einstein’s field can all be placed comfortably within the hyperspace field. We see that these fields fit together precisely within the hyperspace field like pieces in a jigsaw puzzle. The other advantage of field theory is that it allows us to calculate the precise energies at which we can expect space and time to form wormholes. Unlike the ancients, therefore, we have the mathematical tools to guide us in building the machines that may one day bend space and time to our whims.

Does this mean that big-game hunters can now start organizing safaris to the Mesozoic era to bag large dinosaurs? No. Thorne, Guth, and Freund will all tell you that the energy scale necessary to investigate these anomalies in space is far beyond anything available on earth. Freund reminds us that the energy necessary to probe the tenth dimension is a quadrillion times larger than the energy that can be produced by our largest atom smasher.

Twisting space-time into knots requires energy on a scale that will not be available within the next several centuries or even millennia—if ever. Even if all the nations of the world were to band together to build a machine that could probe hyperspace, they would ultimately fail. And, as Guth points out, the temperatures necessary to create a baby universe in the laboratory is 1,000 trillion trillion degrees, far in excess of anything available to us. In fact, that temperature is much greater than anything found in the interior of a star. So, although it is possible that
Einstein’s laws and the laws of quantum theory might allow for time travel, this is not within the capabilities of earthlings like us, who can barely escape the feeble gravitational field of our own planet. While we can marvel at the implications of wormhole research, realizing its potential is strictly reserved for advanced extraterrestrial civilizations.

There was only one period of time when energy on this enormous scale was readily available, and that was at the instant of Creation. In fact, the hyperspace theory cannot be tested by our largest atom smashers because the theory is really a theory of Creation. Only at the instant of the Big Bang do we see the full power of the hyperspace theory coming into play. This raises the exciting possibility that the hyperspace theory may unlock the secret of the origin of the universe.

Introducing higher dimensions may be essential for prying loose the secrets of Creation. According to this theory, before the Big Bang, our cosmos was actually a perfect ten-dimensional universe, a world where interdimensional travel was possible. However, this ten-dimensional world was unstable, and eventually it “cracked” in two, creating two separate universes: a four- and a six-dimensional universe. The universe in which we live was born in that cosmic cataclysm. Our four-dimensional universe expanded explosively, while our twin six-dimensional universe contracted violently, until it shrank to almost infinitesimal size. This would explain the origin of the Big Bang. If correct, this theory demonstrates that the rapid expansion of the universe was just a rather minor aftershock of a much greater cataclysmic event, the cracking of space and time itself. The energy that drives the observed expansion of the universe is then found in the collapse of ten-dimensional space and time. According to the theory, the distant stars and galaxies are receding from us at astronomical speeds because of the original collapse of ten-dimensional space and time.

This theory predicts that our universe still has a dwarf twin, a companion universe that has curled up into a small six-dimensional ball that is too small to be observed. This six-dimensional universe, far from being a useless appendage to our world, may ultimately be our salvation.

It is often said that the only constants of human society are death and taxes. For the cosmologist, the only certainty is that the universe will one day die. Some believe that the ultimate death of the universe will come in the form of the Big Crunch. Gravitation will reverse the cosmic expansion
generated by the Big Bang and pull the stars and galaxies back, once again, into a primordial mass. As the stars contract, temperatures will rise dramatically until all matter and energy in the universe are concentrated into a colossal fireball that will destroy the universe as we know it. All life forms will be crushed beyond recognition. There will be no escape. Scientists and philosophers, like Charles Darwin and Bertrand Russell, have written mournfully about the futility of our pitiful existence, knowing that our civilization will inexorably die when our world ends. The laws of physics, apparently, have issued the final, irrevocable death warrant for all intelligent life in the universe.

According to the late Columbia University physicist Gerald Feinberg, there is one, and perhaps only one, hope of avoiding the final calamity. He speculated that intelligent life, eventually mastering the mysteries of higher-dimensional space over billions of years, will use the other dimensions as an escape hatch from the Big Crunch. In the final moments of the collapse of our universe, our sister universe will open up once again, and interdimensional travel will become possible. As all matter is crushed in the final moments before doomsday, intelligent life forms may be able to tunnel into higher-dimensional space or an alternative universe, avoiding the seemingly inevitable death of our universe. Then, from their sanctuary in higher-dimensional space, these intelligent life forms may be able to witness the death of the collapsing universe in a fiery cataclysm. As our home universe is crushed beyond recognition, temperatures will rise violently, creating yet another Big Bang. From their vantage point in hyperspace, these intelligent life forms will have front-row seats to the rarest of all scientific phenomena, the creation of another universe and of their new home.

Although field theory shows that the energy necessary to create these marvelous distortions of space and time is far beyond anything that modern civilization can muster, this raises two important questions: How long will it take for our civilization, which is growing exponentially in knowledge and power, to reach the point of harnessing the hyperspace theory? And what about other intelligent life forms in the universe, who may already have reached that point?

What makes this discussion interesting is that serious scientists have tried to quantify the progress of civilizations far into the future, when space travel will have become commonplace and neighboring star systems
or even galaxies will have been colonized. Although the energy scale necessary to manipulate hyperspace is astronomically large, these scientists point out that scientific growth will probably continue to rise exponentially over the next centuries, exceeding the capabilities of human minds to grasp it. Since World War II, the sum total of scientific knowledge has doubled every 10 to 20 or so years, so the progress of science and technology into the twenty-first century may surpass our wildest expectations. Technologies that can only be dreamed of today may become commonplace in the next century. Perhaps then one can discuss the question of when we might become masters of hyperspace.

Time travel. Parallel universes. Dimensional windows.

By themselves, these concepts stand at the edge of our understanding of the physical universe. However, because the hyperspace theory is a genuine field theory, we eventually expect it to produce numerical answers determining whether these intriguing concepts are possible. If the theory produces nonsensical answers that disagree with physical data, then it must be discarded, no matter how elegant its mathematics. In the final analysis, we are physicists, not philosophers. But if it proves to be correct and explains the symmetries of modern physics, then it will usher in a revolution perhaps equal to the Copernican or Newtonian revolutions.

To have an intuitive understanding of these concepts, however, it is important to start at the beginning. Before we can feel comfortable with ten dimensions, we must learn how to manipulate four spatial dimensions. Using historical examples, we will explore the ingenious attempts made by scientists over the decades to give a tangible, visual representation of higher-dimensional space. The first part of the book, therefore, will stress the history behind the discovery of higher-dimensional space, beginning with the mathematician who started it all, Georg Bernhard Riemann. Anticipating the next century of scientific progress, Riemann was the first to state that nature finds its natural home in the geometry of higher-dimensional space.

Magic is any sufficiently advanced technology.

Arthur C. Clarke

ON June 10, 1854, a new geometry was born.

The theory of higher dimensions was introduced when Georg Bernhard Riemann gave his celebrated lecture before the faculty of the University of Göttingen in Germany. In one masterful stroke, like opening up a musty, darkened room to the brilliance of a warm summer’s sun, Riemann’s lecture exposed the world to the dazzling properties of higher-dimensional space.

His profoundly important and exceptionally elegant essay, “On the Hypotheses Which Lie at the Foundation of Geometry,” toppled the pillars of classical Greek geometry, which had successfully weathered all assaults by skeptics for 2 millennia. The old geometry of Euclid, in which all geometric figures are two or three dimensional, came tumbling down as a
new
Riemannian geometry emerged from its ruins. The Riemannian revolution would have vast implications for the future of the arts and sciences. Within 3 decades of his talk, the “mysterious fourth dimension” would influence the evolution of art, philosophy, and literature in Europe. Within 6 decades of Riemann’s lecture, Einstein would use four-dimensional Riemannian geometry to explain the creation of the universe and its evolution. And 130 years after his lecture, physicists
would use ten-dimensional geometry to attempt to unite all the laws of the physical universe. The core of Riemann’s work was the realization that physical laws simplify in higher-dimensional space, the very theme of this book.

Ironically, Riemann was the least likely person to usher in such a deep and thorough-going revolution in mathematical and physical thought. He was excruciatingly, almost pathologically, shy and suffered repeated nervous breakdowns. He also suffered from the twin ailments that have ruined the lives of so many of the world’s great scientists throughout history: abject poverty and consumption (tuberculosis). His personality and temperament showed nothing of the breath-taking boldness, sweep, and supreme confidence typical of his work.