Warped Passages - Lisa Randall [140]
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 (see Figure 67).
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.
Figure 67. An open string and a closed string.
For both open and closed strings, the resonant modes are those that oscillate an integer number of times along the string’s length. A few such modes are depicted in Figure 68. 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.
Figure 68. Some string oscillation modes for (above) an open and (below) a closed string.
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 particles, which are relatively light, arise from strings with the fewest oscillations. A mode with no oscillations could be a familiar light particle, such as an ordinary quark or 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. But for now, let’s review the conventional string theory picture. We’ll catch up with extra-dimensional models later on.
String Theory’s Origins
By the future Ike XLII’s time, string theory could boast quite a long history. But for scientific purposes, we’ll confine our story to the twentieth and early twenty-first centuries. We now think of string theory as a theory that might reconcile quantum mechanics and gravity. Originally, however, it had a completely different application. The theory first emerged in 1968 as an attempt to describe the strongly interacting particles known as the hadrons. That theory was not successful; as we saw in Chapter 7, we now know that hadrons are made from quarks held together through the strong force.