KNOTTY OLD ISSUE KNOTTY OLD ISSUE "Mathematics are well and good but nature keeps dragging us around by the nose," Albert Einstein groused, a lament that echoes in the debate over string theory. Physicist Lee Smolin has criticized this theory as a mathematical effort to solve a problem that belongs in the realm of theorists. He sees a historical warning in the mathematics of "knot theory." Knot theory was the offspring of eminent physicist Lord Kelvin's 1860's idea that atoms are essentially knots in the aether. Aether was a mysterious fixed medium through which light traveled, in the minds of Victorian scientists. Kelvin's concept was popular for decades, sparking the Scottish physicist Peter Tait to devise a table of the elements based on knots, with heavier, more complex ones representing heavier atoms. (Hydrogen was a simple loop and lead a complex one, for example.) Knot theory’' relevance to atomic physics was untied by later experiments before Einstein's landmark 1905 "e=mc2" papers proved its final undoing. "But they guessed wrong about nature, not about mathematics," says Peter Ewing of the American Mathematical Society. Knot theory has many non-physics applications and is a thriving subject, he says. Ewing says Kelvin and Tait's error says little about string theory because the two ideas don't share the same underlying math. Besides, history is filled with math ideas that were busts, he notes, from the ancient Pythagoreans' notion that numbers have gender to the "epicycles" that medieval astronomers used to explain planetary motion. They "only say something about our limitations in making good guesses about nature," he says. See a graphic illustrating knot theory at http://www.math.buffalo.edu/~menasco/knottable.gif Dan Vergano String theory: Hanging on by a thread? String theory is on the ropes. After decades of prominence as the key to physics' elusive "theory of everything," challengers say the hypothesis is unraveling. Why? Because there haven't been experiments to prove it — and there don't seem to be any on the horizon. "The interplay with experiments is essential, and string theory just doesn't have that," says physicist Lee Smolin, author of The Trouble With Physics: The Rise of String Theory, the Fall of Science, and What Comes Next, out today Physics breakthroughs power advances in areas as diverse as computing, material science (nanotechnology) and electronics, and Smolin says it's bad news for progress if physics goes off track. For decades, some scientists, most notably Albert Einstein, have sought a "theory of everything" to unite the fundamental theories of physics: general relativity (which geometrically models gravity as massive objects bending the fabric of space, leading them to follow curved orbits), electromagnetism and quantum mechanics (which explains atomic forces as the result of point-like atomic particles working together in wave-like fashion). The last great triumph of 20th-century physics was the so-called standard model of particle physics, which linked electromagnetic and atomic forces by showing they all result from the interactions of fundamental sub-atomic particles. These point-like objects with whimsical names like "quarks," "leptons" and "bosons" are the building blocks of atoms, according to the standard model. But general relativity's gravity remains distinctly divorced from the standard model, a quandary that has long troubled physicists because the two theories differ greatly in their visions of how the universe functions and fits together. This suggests that both fundamental theories are fundamentally flawed, say Smolin and others. Enter string theory, which surfaced in 1970 with the research of the University of Chicago's Yoichiro Nambu. Broadly speaking, string theory envisions subatomic particles as strings and loops of vibrating energy rather than the point-like particles of the standard model. Each string may be about a billion billion times smaller than the protons inside atoms. The appeal of string theory, says physicist Sean Carroll of the California Institute of Technology, is that these little energy loops appear to mathematically explain not only the interactions of atomic particles but also where gravity comes from. String theory describes a vibrating string that acts like a "graviton," which produces the force of gravity, much in the same way that the standard model's particles produce forces. But it wasn't until 1984 that theorists John Schwartz of the California Institute of Technology and Michael Green of England's Cambridge University showed that string theory's mathematics could encompass all the particles in the standard model, not just parts of it. The finding captivated physicists. But Smolin says its adherents are prizing mathematical agility, the theoretical ability to whip up ever more stringy particles, over deep insight into the mismatch between gravity and other forces. "Aspects of string theory may turn out to be true," Smolin says, but physicists have flirted with failed mathematical bridges to nowhere, built of string-theory buttresses such as extra dimensions and elegant math, throughout the last two centuries. In particular, Smolin charges that string theorists just fudged their models to explain away dark energy — a mysterious force that supernova measurements indicate is pulling galaxies away from one another at an accelerating rate — rather than admitting they have real problems. Other detractors, including physicists Lawrence Krauss, author of last year's Hiding in the Mirror: The Mysterious Allure of Extra Dimensions From Plato to String Theory and Beyond, and mathematician Peter Woit, author of this summer's Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law, argue that string theory is dragging physics down a rabbit hole, producing endless theorizing and no payoff. Physicists always argue, says historian Spencer Weart of the American Physical Society's Center for the History of Physics in Greenbelt, Md. Respectable physicists disagreed about the existence of atoms until the 1950s, he notes, until experiments settled the issue. String theory differs from those cases historically, Weart says, in an inability to come up with experiments. "In the end, physicists like a theory only if it will help them to do some research," Weart says. Schwartz, one of the fathers of modern string theory, replies by e-mail that experiments will verify string theory in the future. The big question is how much energy an experiment would have to pound into a collision between particles to reveal strings, he adds. Many physicists hope that Europe's Large Hadron Collider facility will offer some answers, starting in 2007. Ultimately, Carroll says, "the only way for someone to kill string theory will be to come up with a better one." String theory is physics' great hope for uniting the physics of galaxies (shown left) with the phyiscs of sub-atomic particles. In this artist's illustration, newborn galaxies (white circle) mature into older ones (spirals).



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