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1 Serron: These guitar strings rotating at billions of r.p.m. What are they made of?
1 Salesman: Collapsed degenerate neutronium.
2 Serron: How does the string not fly apart?
2 Salesman: The outside revolves at near light speed, but the centre is stationary.
3 Salesman: The rotating part Lorentz contracts tangentially, reducing the circumference. That squeezes the string, holding it together.
4 Serron: This is very difficult to understand.
4 Salesman: It’s a straightforward application of string theory.
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String theory is a mathematical-physical model that attempts to describe fundamental particles and their interactions.
Before we go any further, I want to make the disclaimer that string theory is pretty complicated, and I am not by any means an expert on it. I never studied it during my formal physics studies, and I only know what I've managed to pick up with casual reading. Nevertheless, I shall now attempt to provide a summary that will hopefully make sense and provide some useful insight for the average person. It's possible that I may make a mistake or misrepresentation, for which I apologise in advance.
Also, there is not just one "string theory" that encompasses everything that scientists have proposed in this field. String theory really refers to a number of different models, all based on the same premise, but then developed in slightly different ways.
The basic premise of all these string theories is the idea that we can treat the point-like particles of physics as one-dimensional objects, rather than as effectively zero-dimensional points. The point-like particles are the leptons (the electron, muon, and tau lepton, plus their respective neutrinos), the quarks, the various vector bosons (which includes the photon, gluon, and W and Z bosons), and the Higgs boson. Notably, this list does not include the more familiar proton and neutron, which are composite particles composed of triplets of quarks.
The one-dimensional objects of string theory are called strings. There are really only two different types of strings: open strings, with two ends like a shoelace, and closed strings, which form a loop like a rubber band. Some models of string theory use both open and closed strings, while some use only closed strings.
The size of a string is very small, postulated to be of the order of the Planck length, about 10-35 metres, which is roughly the distance scale at which we expect quantum mechanics and gravity to interact. This is way too small to be observed with any equipment we have - or possibly even any equipment we could conceivably build. So if we can't see or measure the one dimensional extent of these strings, what's the point of proposing such a thing?
The point is that a one-dimensional object such as a string can vibrate - much like a violin or guitar string. And like those musical strings, a particle string can vibrate in one of a suite of different vibrational modes, with different numbers of nodes and different vibrational frequencies. This is similar to how a bugle player can play different notes with a fixed length of pipe, by varying the vibrational mode by applying different lip pressure to the mouthpiece.
And this is where we regain our family of different fundamental particles. A string vibrating in one mode can appear to be an electron, while vibrating in a different mode it can appear to be a muon, or a neutrino, or perhaps a quark.
The appeal of string theory is that the mathematical modelling of particles as vibrating strings produces expressions for things like the interactions between particles, and those expressions look like the sorts of interactions we already know. For example, a string vibrating in a way that makes it look like an electron has interactions with other strings vibrating in the same way, that result in them being repelled from one another by a force that drops off as the inverse square of the distance between them. In other words, string theory produces a force that looks like the electromagnetic force. And it produces this "for free" - we didn't have to encode the electromagnetic force into string theory up front. It just falls out as a consequence.
As you might expect, this is pretty exciting stuff for physicists. If you make one basic assumption about fundamental particles, you end up producing a bunch of physics that we already know. This is what's convinced many physicists that the mathematical model that is string theory is probably describing something that reflects reality, and how the universe really behaves.
On the other hand, it's very difficult to test any of the aspects of string theory experimentally, or to distinguish which of the many proposed variant string theory models might be closer to describing reality. The general feeling is that there must be something to string theory, but we're not yet sure exactly what. Some sort of catalysing breakthrough is still required for string theory to cement a place as a useful and predictive model with the same sort of stature as Newton's law of gravity, or Einstein's theory of relativity. Some physicists even suggest that string theory is a blind alley, which currently may look promising, but which does not reflect any underlying reality, and may eventually be discarded when (and if) we come up with a better model for describing fundamental particles and their interactions.
So string theory is very much still a developing field, and not an area of science that is fully established.
 Thus, the Planck length is roughly the scale at which we don't really understand the physics of what happens, since we do not yet have a workable model of quantum gravity.
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