Hiding in the Mirror (2 page)

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 may
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.”

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

T
he 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.

One of the people whose critical examination
helped Ampère ultimately refine his theory was the budding physicist
Faraday. The year after Oersted made his discovery, in fact,
Faraday published his own first significant discovery regarding
electricity and magnetism. (Essentially all of his previous work
had been on chemical analysis.) He discovered that small magnets
would rotate around a wire with a current flowing through it, or
alternatively, that a wire with a current flowing in it could be
made to rotate about a fixed magnet. This established the peculiar
nature of the magnetic force that was produced by moving electric
charges, and ultimately verified key aspects of Ampère’s ideas. The
fact that the resulting force between the magnet and the wire was
not merely attractive or repulsive, like the electric force between
charges, but rather, pointed perpendicularly to an imaginary line
joining the two objects (which would make one rotate around the
other) was the first hint that the relationship between electricity
and magnetism would require a completely new way of thinking. The
simple, intuitive world that Newton unveiled with his brilliance
was about to reveal its hidden underbelly.

It is interesting to note that in a letter
written at the time to a friend in Geneva, Faraday talked about his
early reticence in working on the subject associated with Ampère’s
“wild” theories: Theory makes up the great part of what M. Ampère
has published, and theory in a great many points unsupported by
experiments when they ought to have been adduced . . . [F]or
myself, I had thought very little about it before your letter came,
simply because, being naturally skeptical on philosophical
theories, I thought there was a great want of experimental
evidence. Faraday went on to spend the next forty years of his life
providing that evidence, and in what is perhaps one of the more
profound ironies of physics, he ultimately provided the key
theoretical idea that would reveal the true relationship between
electricity and magnetism. While Oersted had shown that the former
could create the latter, as early as 1822 Faraday wrote in his
experimental notebook, where he recorded all his thoughts and
ideas, the suggestion “convert magnetism into electricity.”

Nine years later, on August 30, 1831, Faraday
achieved the longsought goal by means of his most famous
experiment, described at the beginning of this chapter. But while
Faraday demonstrated that magnetism
could
create electricity, it did so in a way that no one had suspected. A
normal magnet, no matter how strong, could not generate an electric
current. However, a magnet whose strength
changed
could produce a current in a nearby wire. In
his initial experiment Faraday created such a changing magnet
simply by turning on and off a current in the first wire. As Oersted
had already established, once a current was flowing in a wire, that
wire acted like a magnet. Thus, during the brief period that the
strength of the current rose from zero to its ultimate value, the
corresponding strength of the magnet that it generated varied
accordingly. It was only on the short interval surrounding the
times that the circuit was either opened or closed in the first wire
that Faraday noticed a current flowing in the second wire.

Faraday verified his idea that it was actually
the changing strength of the magnet that caused a current to flow in
the second wire by conducting a different experiment. Instead of
turning a current on and off in the first wire, he simply moved a
magnet closer and then farther away from the second. A current
flowed as the magnet approached and again as it was withdrawn.

We now call Faraday’s discovery induction,
because one can induce currents to flow in wires exposed to magnets
whose magnetic strength, relative to the wire, is changing. Faraday
was justified in the promise he made Gladstone quoted in the
epigraph to this chapter, because today we do tax this phenomenon,
which has made possible most modern technology, as it allows us to
produce electric power from sources such as falling water. If the
water can be channeled through a tunnel, and made to spin a turbine
holding several magnets within it, as the turbine spins around
currents will be induced to flow in wires surrounding it. This is
how we generate most of the electricity in the area of the United
States where I currently live.

While Faraday’s experimental discoveries
therefore changed the face of modern society, they also changed our
picture of nature. With his highly intuitive sense of nature,
Faraday distrusted simple mathematical descriptions of phenomena,
such as the force of attraction between two magnets. He preferred
instead to formulate a physical “picture” of this force, so as a
visual aid he suggested that throughout the space surrounding the
magnets, one could imagine “lines of force.” The direction of the
force that would be experienced by another magnet that one might
locate at any position would follow along the lines of force
passing nearby. Similarly, the total number of field lines located
near this point would signify the strength of the force. Ultimately
Faraday used the same kind of visualization to describe the
electric forces between charged particles, again without resort to
mathematical equations. Had Faraday been more comfortable with
mathematics, he would have recognized that these “field lines”
themselves had a simple mathematical description in terms that we
now describe as a “magnetic field.” A field is simply a function that
assigns to each point in space some quantity. This quantity can be
something as simple as a single number, or it can be something more
complicated, such as a vector, which is a number plus a direction,
appropriate to describe a force, for example. The idea that magnets
and charges might give rise to magnetic and electric fields,
respectively, represented a major conceptual advance. From the time
of Newton onward the question of how forces such as gravity
actually act on distant objects had been a complete mystery.
So-called instantaneous action at a distance seemed physically
implausible—how did the earth know where the sun was in order to be
attracted to it?—but a necessary, if unpleasant, fact of life.
Faraday’s fields solved this problem, at least in principle. If
electric or magnetic fields exist throughout all of space,
surrounding every charged object or magnet respectively (and for
the moment one could ignore the question of how long it would take
for such fields to develop around each such object), then a charged
object or magnet located at a remote distance from another such
object could experience a force due indirectly to that distant
charge or magnet, but manifested directly via an interaction with
the electric or magnetic field present in its own immediate
vicinity. No direct action at a distance would be required! Faraday
reasoned that gravity, too, could be described in terms of lines of
force, thus avoiding Newton’s conundrum.