We’ve learnt that all strings vibrate as a superposition of modes. Each mode is a particular type of vibration and has an associated energy.
In quantum string theory every mode is identified with a fundamental particle. The equations describing the mode correspond exactly with those defining the particle. For example, the mathematical laws governing photons naturally emerge as the equations for a particular string mode.
This is totally unexpected. String dynamics has nothing to do with electromagnetism, yet Maxwell’s equations appear from nowhere. And that’s not all. The same magic can happens for the other forces of the Standard Model, including the graviton. This is why string theory is a candidate for a fundamental unified theory.
As strings vibrate more and more vigorously, their modes give rise to an infinite number of particles. Einstein’s famous equation E = mc2 tells us that there is an equivalence between energy and mass: the more energetic the string, the heavier the corresponding particle is.
Because fundamental strings are so very small, they form incredibly tight loops and therefore require a colossal amount of energy in order to vibrate. You could pack a million billion billion of these strings into the width of a human hair, but each has the same energy as a train roaring down a track at maximum speed!
So if our strings have such enormous energy, how could they ever correspond to the fundamental particles we observe? Indeed, these have truly tiny masses and thus small energies. Luckily, quantum mechanics comes to the rescue.
Remember the uncertainty principle? It implies that seemingly empty space is filled with energy, called vacuum energy. Physicists worked out that this vacuum energy could cancel with the vibrational energy of the strings, lowering their overall energy and mass.
This cancellation allows vibrating strings to appear as massless, or almost massless, particles. One of string theory’s most celebrated results is that the vibrations of closed strings automatically give a massless particle with all the properties of the elusive graviton. Gravity emerges naturally from string theory!
Only a few of the string modes would correspond to the particles we see around us. There are infinitely many more particles predicted by string theory, far too heavy to detect in our current laboratories. But there could be indirect ways to look for them. If they were to be discovered it would be a huge leap for string theory.
The first string theories had a few problems. They accounted for bosons (such as force particles like the photon) but did not contain fermions (for example matter particles such as the electron) at all. Secondly the mathematics required twenty-six spacetime dimensions! Lastly the theory predicted an impossible particle with negative mass called the tachyon.
Thankfully supersymmetry solved these difficulties. Superstring theory produces fermions as well as bosons and removes the need for an impossible tachyon. It also brings the required dimensions down to ten – nine space and one time.