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Physicists love nothing more than a good puzzle: A counter-intuitive observation or measurement sends theorists scurrying to their computers and experimentalists to their laboratories. A mathematical signal in a new theory launches a scramble of to understand its real-world implications. Two successful theories, each supported by large bodies of observational evidence, seem to be fundamentally incompatible.
Tussling with enigmas like these has been the central theme in the development of physics for more than a century. It has been and continues to be a source of endless fascination for physicists and non-physicists alike.
Is it any wonder, then, that Princeton physics professor Steven S. Gubser opens The Little Book of String Theory with three paragraphs that each begin, "String theory is a mystery"?
That mystery of string theory, he notes, has also been a source of controversy. The theory originally proposed that the behavior of nature's fundamental particles and forces (except gravity) can be derived from the vibrations of nearly infinitesimal strings in a universe with many additional dimensions beyond the familiar three of space and one of time. The idea remains attractive, but after nearly 40 years, it has yet to be verified by experiments or observations. "It's all about extra dimensions, quantum fluctuations, and black holes. How can that be the world?" Gubser asks. "Why can't everything be simpler?" [p.1]
Yet a resurgent string theory has twice grabbed center stage among theoretical physicists. First came superstring theory in 1980 that connected strings to gravity. Then in 1995 came "branes" that suggested new relationships between physical reality and the computations of string theory.
"(C)alculation after calculation yields unexpectedly beautiful results...," notes Gubser. "How can this not be the world? How can such deep truths fail to connect to reality?"
But they have failed to connect--at least so far. It is now more correct to speak of multiple string theories than of a single one. Its advocates say that we only need to figure out which one describes the universe. That will be the long-sought "theory of everything."
Its detractors argue that having a multiplicity of theories with no reason to choose any one of them makes it the "theory of anything" instead. In 2006, a pair of books argued that string theory may have reached the end of its skein.
Smolin's assessment was rosy in comparison to the critique offered by Columbia University mathematician Peter Woit in Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law. Woit's title recalls a famous remark by the sharp-tongued Wolfgang Pauli describing a particularly poorly conceived paper. String theory is not even wrong, Woit asserts, because each refinement seems to lead physicists further astray.
Gubser deliberately leaves out the names of string theorists to focus on ideas rather than personalities. Yet, whether he intends it or not, The Little Book of String Theory is a response to both Smolin's and Woit's pessimistic conclusions.
"In the end," Gubser asserts, "the proponents and the critics... are not that far apart on matters of substance. Everyone agrees that there are some deep mysteries in fundamental physics. Nearly everyone agrees that string theorists have mounted serious attempts to solve them. And surely it can be agreed that much of string theory's promise has yet to be delivered upon."
Gubser's book responds to Smolin's and Woit's in another way as well. Theirs are filled with discussions that leave non-mathematical readers struggling to make sense of extra curled up dimensions of space-time and the implications of symmetries in those additional dimensions.
In contrast Gubser's approach is to replace mathematics with analogies. Quantum mechanical wave functions, for example, relate to one of his favorite pieces of classical music, Chopin's Fantasie-Impromptu. And to explain the concept of mathematical duality, he invokes images of Fred Astaire and Ginger Rogers on the dance floor. If you see only one, you can deduce the motion of the other.
Still, string theory and its terminology are inherently mathematical and esoteric. Despite Gubser's best efforts, most readers will still wrestle with essential concepts from physics like gauge theories, tachyons, renormalizability, supersymmetry (including broken supersymmetry), and the temperature of black holes. They will have to grapple with distinctions among D0-, D1-, D3-, and higher dimensional D-branes, and their connections to the great questions of physics.
When too many of those show up in the same paragraph, most readers are likely to wonder whether they are understanding any of this. An example: "Back to S-duality. I introduced it by saying that strings are exchanged with D1-branes. It turns out that D5-branes are exchanged with solitonic 5-branes, and D3-branes are unaffected by the duality. What this means is that you start with one string on one side of S-duality, you end up with a D1-brane on the other side; but if you start with a D3-brane on one side, you end up with a D3-brane on the other."
Readers with some background in physics will respond differently. They will want to see the math.
Fortunately, such difficult sections are rare enough that lay readers can skim past them. And the physics enthusiasts can use them as a jumping off point to sections of the Smolin and Woit books.
Overall, The Little Book of String Theory succeeds in its mission to carry readers through the tangle of ideas to the intellectual loose ends that physicists love. "Without a doubt, string theory is an unfinished canvas," Gubser concludes. "The big question is, when the results get filled in, will the resulting picture reveal the world?"