Warped Passages: Unraveling the Mysteries of the Universe's
Hidden Dimensions. Lisa Randall. xii + 500 pp. Ecco Press,
Parallel Worlds: A Journey Through Creation, Higher Dimensions,
and the Future of the Cosmos. Michio Kaku. xviii + 428 pp.
Doubleday, 2005. $27.95.
The fact that space has three dimensions would seem to be one of the
most obvious and indisputable features of our world. Ever since
Einstein proposed his theory of general relativity, however, it has
been possible to imagine the existence of extra, somehow hidden,
dimensions—new directions in which material objects could
extend in space. Their existence is often considered in the context
of a desire to unify gravitation with other forces, a goal that
continues to be important. String theory, the leading candidate for
reconciling quantum mechanics with general relativity, actually
requires the existence of extra dimensions. Over the course of the
last few decades, theoretical physicists have invested great effort
in exploring the different ways in which such dimensions could be
hidden from view and what effect they might have on the physics we
Lisa Randall, who has been one of the most influential researchers
in this area, has written a book aimed at sharing the excitement of
recent discoveries with a general audience. Warped Passages:
Unraveling the Mysteries of the Universe's Hidden
Dimensions follows in the footsteps of popular accounts of
cutting-edge physics by the likes of Stephen Hawking, Kip Thorne,
Alan Guth and Brian Greene, who helped create the ideas they are
explaining. Part of the role of such books is to provide an expert's
view of the current situation in fundamental physics. Equally
important, however, is the insight they give into the thought
processes of working scientists.
The simplest way to hide extra dimensions from view is to imagine
that they are "compactified"—curled up into a tiny
ball (or other geometrical configuration) with an extent much
smaller than what can be probed by current experimental apparatus.
In the 1990s, however, a new possibility arose, as scientists came
to appreciate the role of "branes" in higher-dimensional
physics. A brane, generalizing the concept of a membrane, is simply
an extended object: A string is a one-dimensional brane, a membrane
is a two-dimensional brane, and so on, up to however many dimensions
may exist. A remarkable feature of such objects is that particles
may be confined to them, unable to escape into the surrounding
space. We can therefore imagine that our visible world is a
three-dimensional brane, embedded in a larger universe into which we
simply can't reach.
Gravity, as the curvature of spacetime itself, is the one force that
is hard to confine to a brane; the extra dimensions must therefore
have some feature that prevents gravity from appearing
higher-dimensional. (For example, in four spatial dimensions, the
gravitational force would fall off as the distance cubed, rather
than the distance squared.) One possibility, proposed by Nima
Arkani-Hamed, Savas Dimopoulos and Georgi ("Gia") Dvali,
is that the extra dimensions curl up into a ball that is small
without being too small—perhaps as large as a millimeter
across in each direction. Randall, in collaboration with Raman
Sundrum, showed that an extra dimension could be infinitely
big, if the higher-dimensional space was appropriately
"warped" (hence the title of her book). These scenarios,
and others that followed, launched a renaissance in the study of
extra dimensions. Most intriguingly, these theories made specific
predictions for the outcome of experiments that could be done in the
near future. (Already, the "millimeter" of the original
proposal of Arkani-Hamed and colleagues has been reduced to less
than a tenth of a millimeter by experimental progress.)
Building up to these developments requires a good deal of
background, and Randall's book provides it in great depth. She
begins with an extended introduction to the idea of extra dimensions
itself, including the inevitable invocation of Edwin Abbott's
classic 1884 novel Flatland, which describes a
two-dimensional universe whose inhabitants can't imagine a third
dimension. But then Randall backs up a bit, to launch a detailed
survey of 20th-century physics, covering relativity, gravitation,
quantum mechanics, particle physics, the Standard Model and
extensions thereof, such as supersymmetry and string theory. She
makes a concerted effort to keep the presentation lively and
entertaining—by, for example, quoting from popular music and
featuring fictional characters, Athena and Icarus, in certain
narrative digressions. A distinctive feature of Warped
Passages is the discussion of two different ways of extending
physics beyond the Standard Model: the bottom-up, model-building
"Harvard" approach; and the top-down, string-theory
"Princeton" approach. Both philosophies are interesting
and important, and the study of extra dimensions has brought them
into close collaboration. The perspective of someone who has been
immersed in the details makes the discussion of this dichotomy an
especially valuable feature of the book.
Michio Kaku's Parallel Worlds: A Journey Through Creation,
Higher Dimensions, and the Future of the Cosmos, although
superficially similar to Randall's book, actually differs
significantly from it. Although Kaku worked on string theory in its
early days, he has become well known more recently as a popularizer
of physics, and this is evident from the text. Parallel
Worlds is not written from the viewpoint of an insider relating
developments as they occurred. It is telling, for example, that the
bibliography consists solely of other books for a general audience,
with no citations of the primary literature. Nonetheless, the
presentation is extremely polished, and the discussion is
invigorated by the inclusion of numerous interesting and revealing
anecdotes about the participants.
Kaku is also very attuned to the fact that what interests the
general reader is not always what interests the professional
physicist. He is quite willing to discuss the possibility of life on
other planets, or even the religious implications of the work he
describes. Statements such as "If true, [the multiverse] would
unify two of the great religious mythologies, Genesis and Nirvana.
Genesis would take place continually within the fabric of timeless
Nirvana" are made as straightforwardly as comments on the
cosmic microwave background.
The book deals with "parallel worlds" in a somewhat
generalized sense; brane-world scenarios are discussed, but so are
the "many worlds" of the Everett interpretation of quantum
mechanics, as well as the "pocket universes" implied by
inflationary cosmology. Kaku also discusses the recent astronomical
discovery that the expansion of our universe is accelerating, and
the implied existence of dark energy. The notion that galaxies are
flying away from one another at increasing rates as the universe
grows increasingly empty propels the narrative: Can we use other
worlds as a possible escape hatch from this desolate future? The
accompanying discussion, invoking wormholes and baby universes, goes
a step or two beyond established physics. By itself this sort of
speculation is okay, but it blurs an important line. The branes and
extra dimensions of Randall's book, although they seem far-fetched,
arise out of a sober and systematic exploration of the possibilities
opened up by string theory; thus they are concepts that
experimentalists take very seriously. Wormholes connecting different
universes sound no more speculative than extra dimensions but are
actually not nearly as grounded in well-established physics.
Nonexperts may not be able to make these sorts of distinctions.
Both of these books do an excellent job of explaining very esoteric
concepts. As a theoretical physicist myself, I would be cheered to
notice someone sitting at my local coffee shop engrossed in either
book. Parallel Worlds is somewhat easier to dip into and
provides a nice overview of many interesting ideas in modern
physics. Warped Passages, however, is useful and important
both as an introduction to some key ideas in modern physics and as a
window onto the way that physics is really done. Let us hope that
the tradition of accessible books written for the general public by
accomplished scientists continues to thrive.
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