Welcome to the theory where everything is made of strings. They’re much as you might imagine from everyday life; strings can wiggle and contort in myriad ways. In doing so they give rise to particles and forces. Remarkably, the motion of a string can encode both particles and forces.
To understand string theory we must study the physics of strings. It’s good to start with a musical example: you’re playing guitar in a rock band. It’s a huge gig and the crowd is expectant. Once the noise has died down you pluck your first string. It begins to move, producing a characteristic musical note.
As you play, your fingers cause other strings to vibrate. Depending on their shape and size they sound at different pitches. The overall effect is a breathtaking display of harmony and rhythm; it’s no wonder you guys are so successful. And all because of some vibrating strings.
The analogy with string theory is immediate. The guitar strings become the fundamental strings of nature. These vibrate in different ways depending on their length and energy. The different musical pitches correspond to individual particles. The harmonies of the band represent interactions between these particles.
It turns out that these fundamental strings are probably incredibly small. The best estimate for a typical string length is 10-33 cm. This length is often called the Planck scale. If you were to lay a thousand billion billion strings end to end you would only just cover the width of a single atom. They are too minuscule to be detected by our current accelerators. This means that we must look for experimental evidence indirectly.
We partition strings into two categories. Open strings have two endpoints. These might be fixed like on a guitar or could be free to move as they please. Fixing the endpoints in particular ways gives rise to distinct vibrational patterns. Closed strings have no endpoints and so form a complete loop.
A rubber band is a good model for a string. Vibrations involve the band stretching and compressing. The tension in the rubber provides the energy to drive the motion. The tiny fundamental strings require huge tension to keep them small. Correspondingly they oscillate with very large energies.
By Einstein’s famous equation E = mc2 we know that energy is equivalent to mass. Hence a high energy string is the same as a very heavy string. The typical mass of a string is astronomical compared to that of a proton. But if strings are so heavy how can they possibly constitute elementary particles? Fortunately quantum corrections sort out the issue.
So how do strings vibrate? Unsurprisingly they undulate like waves. You can easily see this with a skipping rope. Fix one end of the rope and hold the other. By moving your arm quickly you can send a wave along the material. Different movements create complex patterns of several waves added together. Physicists call this phenomenon a superposition of waves.
So a string sways as a superposition of different oscillations. Each constituent vibration is known as a mode. Adding up all the modes gave you the complex dynamics of the skipping rope. The same is true of our microscopic strings. We can now precisely explain how strings produce particles.