String Training

By Lisa Randall

String Training

The following is excerpted from Warped Passages by Lisa Randall. All rights reserved. No part of this book may be used or reproduced without written permission from HarperCollins Publishers, 10 East 53rd Street, New York, NY 10022.

String theory’s view of the fundamental nature of matter differs significantly from that of traditional particle physics. According to string theory, the most basic indivisible objects underlying all matter are strings—vibrating, one-dimensional loops or segments of energy. These strings, unlike violin strings, say, are not made up of atoms which are in turn made up of electrons and nucleons which are in turn made up of quarks. In fact, exactly the opposite is true. These are fundamental strings, which means that everything, including electrons and quarks, consists of their oscillations. According to string theory, the yarn a cat plays with is made of atoms that are ultimately composed of the vibrations of strings.

String theory’s radical hypothesis is that particles arise from the resonant oscillation modes of strings. Each and every particle corresponds to the vibrations of an underlying string, and the character of those vibrations determines the particle’s properties. Because of the many ways in which strings can vibrate, a single string can give rise to many types of particle. Theorists initially thought there was only a single type of fundamental string that is responsible for all known particles. But that picture has changed in the last few years, and we now believe that string theory can contain different, independent types of string, each of which can oscillate in many possible ways.

Strings extend along a single dimension. At any given time, you need only one number to identify a point along a string, so according to our definition of dimensionality, strings are one-(spatial) dimensional objects. Nonetheless, like real, physical pieces of string, they can curl up and loop around. In fact, there are two types of string: open strings, which have two endpoints, and closed strings, which are loops with no ends.

Which particles a string actually produces depends on the string’s energy and on the precise vibrational modes that are excited. Modes of a string are like the resonant modes of a violin string. You can think of the oscillations as elementary units that can be combined to form all known particles. In this language, particles are chords and their interactions are harmonies. The string of string theory doesn’t always produce all particles, just as a violin string doesn’t produce any sound until someone applies a bow. But just as a bow excites the modes of a violin, energy will excite the modes of a string. And when the string has enough energy, it will produce different particle types.

For both open and closed strings, the resonant modes are those that oscillate an integer number of times along the string’s length. For these modes, the wave oscillates up and down some number of times, with all oscillations completed over the length of the string. For an open string, the wave vibrations hit the end of the string and turn around, going back and forth, whereas waves on closed strings oscillate up and down as they wind around the closed string loop. Any other waves—those that don’t complete an integer number of oscillations—won’t occur.

Ultimately, the precise way that the string oscillates determines all of a particle’s properties, such as its mass, spin, and charge. In general, there will be many copies of particles with the same spin and charge, all with different masses. Because of the infinite number of such modes, a single string can give rise to an infinite number of heavy particles. Known particle, which are relatively light, arise form strings with the fewest oscillations. A mode with no oscillations could be a familiar light particle, such as an ordinary quark or a lepton. But an energetic string can oscillate in many ways, so string theory is distinguished by its heavier particles, which arise from higher vibrational modes.

However, more oscillations require more energy. The extra particles from string theory that arise from more oscillations are likely to be extremely heavy—an enormous amount of energy would be required to produce them. So even if string theory is correct, its novel consequences are likely to be extremely difficult to detect. Since we don’t expect to produce any of the new heavy particles at accessible energies, we expect string theory and particle physics to give rise to the same observable consequences at the energies we see. This picture might change if some of the recent developments about extra dimensions are correct.

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Lisa Randall is a leading theoretical physicist and expert on particle physics, string theory, and cosmology. She works on one of the two main competing models of string theory in the quest to explain the fabric of reality, and was the first tenured woman in the Princeton physics department and the first tenured woman theoretical physicist at MIT and Harvard. Her work has attracted enormous interest and is among the most cited in all of science.