## Math in the Physical Sciences## Modern Physics and Mathematics |

## What are superstrings? |

Amazing as it sounds, one of the most fascinating discoveries in our universe started with an instrument’s vibrating strings. These structures are called superstrings and are often compared to a string on a musical instrument, such as a violin. The musical notes made by the string are said to be excitation modes of the string under tension. In string theory, the observed elementary particles in a particle accelerator could be considered the excitation modes of elementary strings. But unlike the violin, super-strings are floating in space-time; they also have tension like the violin without being tied to anything.

Greek mathematician and philosopher Pythagoras of Samos (c. 582-c. 507 B.C.E.), an expert on the lyre, was probably the first “string theorist,” as he figured out the (mathematical) harmonic relationship of the strings. He determined that vibrating lyre strings with equal tension but different lengths would produce harmonious notes (such as a middle C and a high C) if the ratio of the lengths of the two strings was a whole number. Eventually, mathematicians took Pythagoras’s ideas to new heights, more precisely encoding the harmonics with complex mathematics.

And, of course, there are other mathematical calculations and measurements used when talking about superstrings. For example, the tension in string theory is denoted by the quantity /(2 p a'), in which a' is said to be “alpha prime” and equal to the square of the string length scale. There is also the size of the string (equal to the Planck length, or about 10^{-33} centimeters) and supersymmetry (for every particle that transmits a force, there is a corresponding particle that makes up matter).