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Strings and Things
A brief account of supersymmetry and string theory.
Kaluza-Klein theory is the earliest of the constituent theories. The idea here is to try to unify electromagnetism and gravity by working with a five dimensional spacetime. The extra dimension is postulated to be wrapped up into a little circle that is too small to be seen directly. The metric in the five dimensional spacetime can be broken up into a metric for the usual four dimensional spacetime and two extra bits: the metric components for the fifth dimension, which looks like an electromagnetic field, and a scalar field. The key idea that string theory gets form K-K theories is that internal quantum numbers (e.g. charge or colour) can be caused by spacetime symmetries in extra "compactified" dimensions.
Supersymmetry is a symmetry that pairs up fermions and bosons with each other. Each of the familiar fermions (quarks, electrons, neutrinos) has a new boson partner (squarks, selectrons, sneutrino); and each of the familiar boson (photons, gluons, Ws, Zs) with a new fermion partner (photinos, gluinos, Winos, Zinos). This causes each fermion loop in a Feynman diagram (which typically leads to an infinite quantity) to cancel with the boson loop of the particle's supersymmetric partner and vice versa. Even better, making supersymmetry into a local symmetry (i.e. allowing the boson/fermion division to vary from event to event) leads to a theory called supergravity, in which there is a whole bunch of new fields, one of which looks like gravity. Unfortunately there is no experimental evidence for any of this, and the theory predicts lots of new particles.
The old string theory was a theory of the strong force that has since been entirely abandoned in favour of quantum chromodynamics (the theory of quarks and gluons). As far as I know, the idea was that there would be little "open strings" whose tension would be the strong force and whose ends would be hadrons (the particles that feel the strong force). The theory was plagued with spin-2 modes which were a nuisance (but which looked a bit like gravitons, which made some people start thinking about the theory that turned into the modern string theory).
As I've said the theory of superstrings is a collision of all of these cool but wrong ideas. The key attractions seem to be that it promises to unify all the forces and give a theory that involves only finite quantities (essentially by "smearing out" interactions that happen at single events in more traditional theories). The problems are that the mathematics is just too hard for string theorists to make definite predictions about anything. What's more it seems that even if they could then any new phenomena would probably occur at such high energies that we couldn't look for them experimentally anyway. Also, it doesn't really help with any of the conceptual problems of quantum gravity, and it involves a fixed background spacetime structure which seems like a bad idea.