String theory

String theory is a branch of modern high-energy physics that attempts to describe the four fundamental forces of nature within a single theoretical framework.

More specifically, string theorists seek to replace the current Standard Model of particle physics, which describes the electromagnetic, weak and strong nuclear forces and general relativity, which describes gravitational interactions. (But note that the Standard Model already contains special relativity.) In current physics gravity is not treated quantum mechanically, which most physicist think will be required for gravitational processes at high energies. String theory is currently the only internally consistent quantum treatment of gravity

Modern models of String Theory are called Superstring theories as they incorporate all of the known fundamental particles as well as their (hypothetical) supersymmetric partners. Superstring theory only works in ten dimensions of space and one of time. This is actually down from the total of 26 dimensions of the earlier bosonic string theory developed in the late 1960s.

Because string theories as they now stand make few predictions and often lack the ability to be tested with falsifiable experiments, some doubt that they have any relevance to physics at all. Elegance does not guarantee correctness. Nonetheless, while there are other attempts at a Unified Field Theory, string theory has so far received the most attention, both within academia and among the general public.

Why?
Electromagnetic, strong and weak forces are well described by quantum field theory. Quantum electrodynamics addresses the electromagnetic interactions, and quantum chromodynamics describes strong interactions. The electroweak theory describes the unification of the weak and electromagnetic forces. This occurs at high energy levels, or the energy density of the Universe at about 10−12 seconds after the Big Bang. At even higher energy levels, (10−36 seconds after the Big Bang), the electroweak and strong forces are predicted to unify. What is not currently understood is whether those three forces will then unify with gravity as energy densities continue to rise. It's believed that the energy densities necessary for this final unification existed at, or very near, 1 Planck time (10−44 seconds) after the Big Bang. Time periods shorter than 1 Plank time are believed to be fundamentally unknowable, if they even exist at all.

However quantum field theories seem to not be able to model gravity consistently as when gravity is treated as just another quantum field the theory becomes mathematically ill-defined. For this reason current physics treats gravity in a purely classical manner, but physicists think it should have a quantum description like all the other forces. The main attraction of String Theory is that it gives a fully mathematically consistent quantum theory of gravity (although this does not mean it is empirically correct of course) and that interestingly the other forces and matter are automatically part of the model along with gravity.

Many theories exist which attempt to address both the electroweak interaction and the strong interaction (these theories are called "grand unified theories"), and one of them may be proven true by the Large Hadron Collider. Fairly few theories exist which attempt to unify gravity with a Grand Unified Theory — superstring theory is one of these so-called.

The general idea
All quantum theories predict that matter can have many "classical manifestations" in experiments. For example systems treated by Quantum Electrodynamics can manifest as Electric and Magnetic fields in one experiment, for example what are called homodyne detectors. However they can manifest as particles in another, such as in a photodetector. This is a basic aspect of quantum theory called complementarity. In Quantum Chromodynamics the systems can appear as particles, fields or even string-like structures. It was in investigations of these latter aspects of QCD that string theory was first applied. In most quantum theories one aspect of the matter is taken as the main one in which the systems have the "neatest" or "most compact" description. In quantum field theory this is the field aspect, but in String Theory it is the string-like aspects that are taken as primary in this sense. Matter is not "made of little strings" in String Theory no more than it is "made of" fields or particles in other quantum theories. Fields, particles and strings are just classical/macroscopic manifestations of the systems, the novelty in String Theory is taking the string-like aspects to be the ones in which the theory has the neatest description. String theory for example can be formulated using only fields and not strings.

Requiring the string-aspects to be primary like this has several implications like requiring the dimensions of spacetime to be much greater, specifically ten-dimensions. To replicate the observed four-dimensions empirically observed, it is postulated that the extra six dimensions have very small extent. However it turns out one can't just say the extra dimensions are small without breaking String theory, the must have a specific form/shape called a.

However it turns out there isn't just one String theory, but five, each of which postulate different kinds of strings (open ended or closed loops,, type of supersymmetry). Each living in ten dimensions. In the 1980s these five String theories were also joined with an 11-dimensional quantum field theory called supergravity as possible quantum theories of gravity. Although supergravity was later found not to be fully consistent (it would break down at high energies) it was proposed by Theoretical physicist and mathematician (considered by many to be the greatest living physicist ) that the five String theories and Supergravity were just limits of one encompassing 11-dimensional theory called M-theory.

Specifically the String theories arise when one makes the 11th dimension small, i.e. they arise when M-theory is "compressed" or compactified down to 10-dimensions, the different String theories coming from how you do this compactification. Supergravity arises when you keep the dimension count at 11, but lower the energy away from the Planck scale. The name M-theory has gained use as it is suspected that this fundamental theory has the "membrane"-like aspects as primary rather than string-like aspects. It also functions as an ambiguous/jokey name as others think the theory makes heavy use of certain Matrices or is Magic/Mysterious.

Or, it all turns out to be bollocks and (LQG) or some other attempt at a Theory of Everything takes over the academic world. It's hard to say, as empirical evidence for any of these theories has been incredibly difficult to come by. The energy levels needed to investigate phenomena at the Planck scale are far beyond even our theoretical ability to generate. Currently, the Large Hadron Collider is able to "resolve" down to 2.8×10-20 meters. For the string like nature of reality (much less branes, or even the spin networks of LQG) to become more apparent, resolutions orders-of-magnitude closer to the 1.6×10-35 meter Planck length are necessary. That 15 orders-of-magnitude difference is like going from the length of your leg to the diameter of a proton, or the inner radius of the Oort Cloud (~1 ly) to a house.

Stephen Hawking on confirming M-theory by observation: "'M-theory is the only possible unified theory, under certain assumptions, the most important of which is that there should be a relation between forces and matter called supersymmetry. This would predict that elementary particles should appear in pairs. It may be possible to observe this in the Large Hadron Collider, which would go a long way towards confirming M-theory experimentally.'"

Problems
To date, the LHC has found no supersymmetric particles, and without those, everything stated above probably doesn't work. Superstring theory is short on falsifiable predictions, except for the prediction of supersymmetry. Given the energy levels necessary to resolve phenomena near 1 Plank length, experiments capable of making those measurements remain purely theoretical.

Woo
String theory has also been the victim of cranks, becoming in their hands a more modern quantum woo, and of course any resemblance with actual string theory and its arcane mathematical foundations is just coincidental. Basically, if you see anything proposing a relationship with string theory outside of academic journals and reputable popular science sources, it's guaranteed to be woo.