# String theory

- Strings carry waves, “standing waves”
- Strings have resonant frequencies, representing certain levels of energy
- Strings are 1-D structures, can be in loops, and have vibrational modes that define particle properties
- Since string theory only works in 11D, one could say the additional dimensions we do not “see” in our universe are extremely tiny dimensions in which the strings can vibrate (but pretty much nothing else)
- The different vibrational modes of strings produce different particles, analagous to how the strings on a guitar produce different notes

- Gravity appears in string theory nicely, a pro to it as a theory

- Kaluza-Klein theory: general relativity applied in 5-d (4 space, 1 time), yields the same results from our 4d universe, plus 1 extra that looks oddly similar to EM.
- Klein said that the 5th dimension could be wrapped up into a tiny amount of space. One could liken this to the idea that at every point in 3d space (+1 time), there is the additional ability to go
*around*a tiny ring, representing this tiny extra dimension wrapped up into a loop. The idea of being able to move along this ring at any point in 3d space is the same idea as moving through that extra dimension. The important idea behind this extra dimension was that momentum in that looped dimension was equivalent to*electric charge*. So there’s this special additional degree of freedom of “movement” that allows sufficiently small objects (i.e. those that can “fit inside” the tiny extra dimension) to gain electric charge according to their position in this 5d space. (Note that the direction of rotation in this looped dimension corresponded to the sign of the charge). - The immediate question here is: what about all the other dimensions of modern string theory? Do they reduce nicely to other observable effects (like that of EM seen in the 5th dimension)?

- Klein said that the 5th dimension could be wrapped up into a tiny amount of space. One could liken this to the idea that at every point in 3d space (+1 time), there is the additional ability to go
- Modern string theory is inspired by Keluza-Klein, just with vibrating strings and just the right extra dimensions, along with super-symmetry.
- Many apparently diverging super-string theories were developed, but then unified by M theory, all as special cases of a larger idea (with an added dimension).
- Extra (tiny) dimensions in M theory are wrapped, just not in simple loops like Keluza-Klein. Instead they’re wrapped according to complex structures known as Calabi–Yau manifolds, which are high-dimensional geometries in which the strings are expected to live.
- But this is a family of manifolds, and there are ~10^500 different possible topologies defined by different manifolds. Each geometry has different implications, yields different particles with different properties.
- A previous though on this: can this definition of string theory be used as a “universe generator”? If there exists an actual mapping between concrete string manifolds and sets of fundamental particles, what can we learn from arbitrary geometries? Do these even define “semantically correct” universes that would produce any value? Thoughts