Because we have made huge strides in our understanding of the nature of scientific theories in the intervening forty years since Wigner penned his essay, I believe we can safely say that the question he poses is no longer of any great concern to scientists. We understand precisely how different mathematical theories can lead to equivalent predictions of physical phenomena, because some aspects of the theory will be mathematically irrelevant at some physical scales and not at others. Moreover, we now tend to think in terms of “symmetries” of nature, what are reflected in the underlying mathematics. While this once again argues for the importance of mathematics in our understanding of nature, these symmetries themselves seem so fundamental that we expect that any theory that can produce correct predictions must reflect them. Thus, seemingly different mathematical formulations can really be understood to reflect identical underlying physical pictures. There is also a flip side to the discussion regarding the unusual effectiveness of mathematics in describing nature. Not all novel mathematical notions that open new horizons for our imagination have correlatives in the natural world. If that were the case, science would be no more than searching for new mathematics.
The power of mathematics will play a large role in what follows, but when it comes to the relationship between our scientific imagination and reality, elegance or mathematical beauty is by itself not sufficient to generate fruitful science. What matters are results. That is why science isn’t philosophy, and why nature holds the upper hand. As Richard Feynman once put it, science is “imagination in a strait-jacket.” In the end our theories rise and fall based on their successful ability to quantitatively predict the future. Imagination truly rises to the level of beauty in science when it allows one to make predictions about things that one may never have thought were predictable.
To return to Plato’s cave, Socrates pointed out that the unfortunate soul who had literally seen the light would, when dragged back in the cave, appear at first to his former compatriots to be a lunatic. This does not, however, mean that all lunatics have seen the light. Every religious prophet in history, for example, from Moses to Jesus, from Mohammed to Joseph Smith has cloaked his or her revelations in language similar to Plato’s. They all suggest that to see the true nature of the world, we merely have to remove the curtains in front of our eyes. But they cannot all be correct. There are different worlds behind each of their curtains. Which brings us inevitably to another complementary aspect of the human experience that literally depends on the existence of another world: religion. It is perhaps not surprising that one of the most popular Christian writers of the the twentieth century, C. S. Lewis, produced a profoundly successful children’s series, The Chronicles of Narnia, which literally exploited a whole new world hidden just under our noses in order to relay its highly allegorical epic saga. Lewis’s Narnia was not like Tolkien’s Middle Earth, located far, far away and long, long ago. Rather, it could be accessed simply by entering an old wardrobe located in a professor’s cluttered house in the country. This was supposed to be some kind of magic, but it is in a fundamental sense not too different from Bill’s portal through the fourth dimension that aired less than a decade later on the Twilight Zone. Lewis’s fantasy stems from a long tradition that indeed lies in that dimension that spans both science and superstition. There is undoubtedly a deep need within our psyches to believe in the existence of new realms where our hopes and dreams might be fulfilled, and our worst nightmares may lie buried.
Religion is the most obvious manifestation of this innate desire for a universe that may be far richer, and perhaps kinder and gentler, than our material existence belies. Nevertheless, while our longings for a deeper reality are in one sense deeply spiritual, they transcend the purely spiritual. They permeate all aspects of our culture, including the pursuit of science. In order to separate science from superstition, we need to recognize that, like Fox Mulder in The X-Files, we all want to believe. Forcing our beliefs to conform to the realities of nature, however, rather than the other way around, is much more difficult and is really, in my opinion, one of the greatest gifts that science can provide our civilization. The process by which this transformation from imagination to science is made is not always clear-cut, especially when we are embroiled in the middle of it as we certainly are now, at least as far as the possibility of new small or large extra dimensions in nature is concerned. This book will in part provide a timely snapshot of where we are now: of the physical and mathematical motivations for our speculations, the sudden rushes of clarity, and the many frustrating red herrings and dashed expectations. The picture that is emerging is far from being in focus, unlike much of what one might read in the popular press. But not knowing all of the answers, and perhaps more importantly, knowing that one does not know all of the answers, is what keeps the search exciting.
We shall encounter diverse manifestations, developed over several centuries—in art, literature, and science—of the idea that the three dimensions of space that we experience are not all there is. But this topic has in recent years taken on a special urgency, which is why I believe it is worth relating at this time, in an honest way, to a broader audience. Dramatic new theoretical ideas seem to suggest the existence of many extra dimensions, and scientists are at this very moment struggling to determine if they have any relation to the real world.
It is worth stressing this last point. Too often in the media, speculative ideas are treated on the same footing as well-tested ones. As a result, it is sometimes hard to tell the difference between them. This is particularly unfortunate when firmly grounded ideas that are known to accurately describe the physical world (such as evolution and the big bang) are passed off as mere theoretical whims of a group of partisan scientists. One of the most useful tasks a popular exposition of science at the forefront can achieve, it seems to me, is clearly differentiate that which we know yields an accurate description of nature on some scale from those things we have reason to suspect one day might do so. And the worst thing such an exposition can do is confuse the two. In the course of this book I will also attempt to present a “fair and balanced” treatment of string theory (in a “non–Fox News” sense)—the source of most of the recent fascination with extra dimensions—and its offshoots. As we shall see, there are many fascinating theoretical reasons for physicists to be excited about working on these ideas. But that should not obscure the important fact that string theory has yet to demonstrate any definitive connection to the real world and, in fact, is a theory that thus far has primarily succeeded in generating more complex mathematics as time proceeds, any hype notwithstanding.
Because of the deeply ingrained nature of the concepts I want to deal with here, while science will form the core of our narrative thread, this book will present a broader history of ideas. This cultural context for the notion of extra dimensions is almost equally compelling, whether in literature or art. Science is not practiced in a vacuum, and, as I have argued, the very fact that the same ideas crop up, often centuries apart, may be telling us something, if not about the natural world, then at least about the human mind.
But what I ultimately find so striking about this story is a facet of science that mesmerizes me each time I visit a physics laboratory. While nothing may seem more esoteric than the notion of hidden extra dimensions, the scientific basis of all such theoretical speculations follows a sometimes circuitous path that however remains rooted in experiment. This remains true even if these experiments sometimes appear on the surface to be as far removed from these notions as baseball is from brain surgery. Through this roundabout process, scientific progress has nevertheless been unmistakable. We fly in airplanes and launch rockets that explore the outer planets. We develop new medicines that extend our lives. We communicate electronically across the globe in an instant, sending messages that once would have taken weeks or months to arrive. Science is an arena of human affairs where we have every right to demand proof that new ideas work.
While Plato’s beliefs about mathematics ma
y seem distinctly modern, Greek philosophy as a whole was largely impotent in technologically empowering that civilization precisely because empiricism was missing from the equation. Natural philosophy had not yet evolved into science. When it thus comes to the possibility that the three dimensions of space we experience are not all there is, I admit to being an agnostic. There are fascinating scientific and mathematical reasons to at least consider the possibility that our three-dimensional space is but the tip of a vast cosmic iceberg. At the same time, there is as of yet not a single compelling reason to believe that this is actually so.
By exploring the artistic, literary, and scientific bases of our current worldview, and taking the discussion up to the current threshold of our own understanding and our own ignorance, we will encounter some of the most fascinating developments of the human mind and some of the most remarkable discoveries about our own universe. Ultimately, I hope to provide you with a better perspective to help you decide on your own what seems plausible, and why. At this point, I believe it is anyone’s guess.
As we embark on our tour, it may be worth quoting the cautionary advice of Antoine Lavoisier, one of the great scientists of the eighteenth century. Lavoisier was the father of much of modern chemistry but was executed during the French Revolution, which was itself based on an illfounded notion of a “scientific” basis for human affairs. He is best known for his discovery of the profoundly important role of an invisible gas, oxygen, in the chemistry of our world. Regarding the emerging exotic science he helped found, Lavoisier warned: “It is with things that one can neither see nor feel that it is important to guard against flights of imagination.”
C H A P T E R 2
FROM FROGS’ LEGS TO FIELDS
Why sir, there is every possibility that you will soon be able to tax it!
—Michael Faraday to Gladstone when asked about the usefulness of electricity
The scientific realization that space and time might not be quite what they seem emerged from the unlikeliest of places: the nineteenthcentury laboratory of a former bookbinder’s apprentice turned chemist, then physicist, tucked away in the heart of London, over fifty years before Edward Abbott penned his mathematical romance of many dimensions.
Michael Faraday was a common man with an uncommon passion. In his lifetime he refused both a knighthood and the presidency of the Royal Society, preferring to remain, in his words, “just plain Michael Faraday.”
Perhaps his humble background forced him to develop an uncommon intuition about nature or at least an uncommon ability to develop pictorial explanations of natural phenomena that could bring otherwise lofty mathematical notions down to earth. Indeed, he claimed—no doubt sarcastically—to have written down a mathematical equation only once in his lifetime. Whatever its origin, he had an inherent predisposition against theoretical models that strayed even slightly beyond the constraints of experiment. It is thus ironic that Faraday ultimately provided the impetus for the creation of one of the greatest theoretical generalizations in the history of physics, a key that unlocked a door to a hidden universe. That key took a form no one could have anticipated in advance, and involved an act of serendipity in an experiment in a laboratory full of chemicals, wires, batteries, and magnets.
The experiment itself was disarmingly simple. A cloth-covered wire wrapped around one-half of a metal ring was connected to a switch connected to a battery. Another similar wire was wrapped around the other half, but hooked up to a device that could detect the flow of electric current through the wire. Since the two different wires were not in direct contact and the cloth wrapping insulated them from the metal ring, when the switch was closed—causing a current to flow in the first wire—there was no immediate reason to have expected a current to flow in the second. But to his amazement, Faraday discovered that at the precise instant that the first switch was closed, or opened again, and only in the instant when electric current either began or ceased to flow in the first wire, an electric current was mysteriously observed to flow in the second.
The uninitiated reader will at this point have at least two questions: (1) Why on earth did Faraday set up such a weird experiment in the first place? and (2) What has this got to do with space and time? The answers will require us to do some time traveling of our own.
Over half a century before Plato penned The Republic, the Greek playwright Euripides had coined the name magnets for the odd lumps of ore found in the Greek province of Magnesia. The mysterious attraction of these objects to bits of iron fascinated the Greeks as it has fascinated generations of budding scientists in each of the twenty-six centuries since then. The Greeks also discovered another invisible force, one between amber (when rubbed with fur) and bits of wood or fabric. This force did not receive its modern name for almost twenty centuries, however, until in 1600 the British scientist William Gilbert adapted the Greek word for amber, electrum, to its modern form, electric, to describe this strange attraction. Following Gilbert’s own studies, electricity and magnetism became the objects of intense scientific interest over the next two centuries. Electricity yielded to a simple mathematical description first, although it would take almost 170 years before the nature of electric forces between charged objects was fully described. Red herrings, priority disputes, false leads, and theories without experimental basis all complicated the search for a fundamental understanding of these forces, as they sometimes do in science. The Journal de Physique wrote in 1781 words that seem disarmingly familiar in a current context:
“Never have so many systems, so many new theories of the Universe, appeared as during the last few years.”
One of the more colorful episodes in this saga involved two brilliant Italian scientists, Allesandro Volta and Luigi Galvani. The subject of the great debate between these two involved nothing less than frogs’ legs. Galvani had discovered, in 1786, that electrical discharges could cause the leg of a dead frog to convulse. Ultimately, he was even able to make them convulse, simply by touching two different metallic plates to the frog’s nerves. Galvani assumed that this metallic arc released some inherent electricity within the frog itself. Meanwhile, Volta, who had developed sensitive instruments to detect the flow of electric charge, felt instead that somehow the electricity was produced by the contact of the two different metals. Ultimately, he was able to prove that this was in fact the cause of the dancing frogs, but more importantly, in the process he developed the electric battery, which introduced a valuable new tool for both science and technology. In 1800 the American expatriate Count Rumford founded the Royal Institution in London and appointed the twenty-three-year-old chemist Humphrey Davy as its director. In the basement of this building Davy built a huge battery, based on Volta’s principles, which he used to power a host of groundbreaking chemical experiments.
Davy was an imposing figure in British science, and his chemical experiments attracted the attention of scientists and laymen alike. One of these, a young bookbinder’s apprentice, was fascinated with science and devoted his leisure time to its study. After attending a series of lectures given by Davy, Michael Faraday bound his carefully prepared notes in a volume and presented them to the great man, with a humble request to be considered for the position of Davy’s laboratory assistant. In a lesson that many students have since learned—namely, it never hurts to flatter your teacher—Faraday was rewarded with the job of his dreams in that very year, 1813.
Meanwhile, on the Continent, strange new observations were underway that began to illuminate an intriguing hidden connection between the otherwise diverse phenomena of electricity and magnetism. It had long been suspected, given the various resemblances between electricity and magnetism (like charges repel, while opposite charges attract, just as two north or two south poles of magnets repel, while opposite poles attract, etc.), that perhaps these two forces were related in some fashion. In the same year that Faraday joined the Royal Institution as Davy’s assistant, Danish physicist-poet Hans Christian Oersted set out a challenge to himself and others to
demonstrate that electricity and magnetism were indeed related. His quest was rewarded seven years later when he published a remarkable discovery: When an electric current flowed through a wire, it could change the orientation of a nearby compass. Oersted had discovered that electricity, when it flows, could generate magnetism. It is difficult to describe the excitement that reverberated throughout Europe when Oersted announced his findings in a short paper, which was translated into various European languages from Latin within weeks. The day it was published in England, Davy brought it down to the laboratory and began working immediately to reproduce its results. Twenty-five years later Faraday reminisced about the repercussions of Oersted’s work:
“It burst open the gates of a domain in science, dark till then, and filled it with a flood of light.” Once again, it’s the image of moving from darkness to light.
The intense intellectual activity throughout Europe following the publication of Oersted’s research was such that within several weeks the eminent French mathematician and physicist André-Marie Ampère developed a remarkable theory of how electricity could produce magnetism, which he later named electrodynamics. Based on a small amount of experimentation and a lot of guesswork and speculation, Ampère’s original ideas were scattershot, but within a year or two they had come together to form the well-known theory that is quoted in physics textbooks today: Ampère reasoned and demonstrated that if currents running through wires could create magnets, and if magnets attracted or repelled, then two nearby wires with currents flowing in them should be repelled or attracted, depending upon the relative directions of the two currents.
Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Page 2