What is string theory? How can I gether a clear concept about the string theory?

ΒΑRAK SHOSHANI
Graduate Student at Perimeter Institute for Theoretical Physics

So you've read in popular science literature that string theory describes the universe as the string section of a cosmic orchestra, with each note played on the strings corresponding to a different particle. As much as you enjoyed this beautiful analogy, even a layman such as yourself cannot help but feel that there's something fishy going on here. What are strings, what are they made of, and most importantly, if they're like tiny violins floating around, then who the heck is "playing" them?

Well, you've come to the right place.


Disclaimer

Before we begin I should probably write down the following disclaimer (which in a perfect world would be attached to anything written anywhere about string theory): "The following statements refer to a speculative physical theory. There is no proof whatsoever that this theory has anything to do with reality."

What are strings "made of"?

Now that we're clear on that, let's start with what a string is made of. I actually answered that already in my answer to What are strings "made of" in string theory?, so you should read that and come back here after you're done.

Generalizations of the point particle

Welcome back! So, what is a string, you ask? Well, you know particles, right? They have zero dimensions. Why is that? Because they are just points, they have no length, width or height. I can either be exactly on the particle or not. I cannot be at different points on the particle since it is itself just a single point.

Let's draw a graph where one axis is time and the other two are space. This graph thus represents spacetime, although we had to cut down the number of space dimensions to two while the universe actually has three of those (for the simple reason that we can't draw a 4-dimensional graph).

What will we see on this graph after some time has passed? We'll see some kind of curve traced by the particle as it moved. This is called the worldline of the particle. Note that the worldline is one-dimensional (hence "line").


(Image courtesy of Wikimedia Commons.)

Now, string theory basically says: Why stop at zero dimensions? That's quite a low number! Let's aim higher, and talk about strings. They have one dimension. That means that they have a length, but that's all they have. No width or height. That means I can be at one end of the string and walk along it to the other end, but I cannot turn left or right or go up and down on the way there.

What happens if we let a string move around on our spacetime graph? It will trace out a surface. We call this surface the worldsheet of the string. Note that the worldsheet is two-dimensional (hence "sheet").

Why stop at one, though? String theory doesn't discriminate; we can actually use it to also describe objects that have two or more dimensions. These are called branes. They trace out a worldvolume in spacetime; this volume can be of 3 or more dimensions. It turns out that branes always come up in some situations in string theory, whether you want them or not. But this question is about strings, so let's go back to them.

It turns out that the string itself is only of secondary importance in string theory. The really important thing is the worldsheet! Most calculations done in string theory will actually be performed on the worldsheet, and not the string, which is merely the "snapshot" of the worldsheet at a particular moment in time. (So maybe it should actually be called "worldsheet theory". But I digress...)

The string spectrum

How do particles come out of strings, you ask? Are they like violin strings that play different notes? Well, not quite. Violin strings are classical objects. Not because they're used in classical music, but because they are not described by quantum mechanics. Strings, on the other hand, are quantum objects. In fact, they are the quantum objects, at least according to string theory.

What does this mean? It means you can't take a string in string theory and "pluck" it. Instead, strings have quantum states (like everything else in quantum mechanics has quantum states). Maybe you would like to read my answer to In layman's term, what is a quantum state? before we continue.

So, these states of the string, it turns out there's an infinite number of them. Each corresponds to a particle with different mass, spin and other properties. Some people like to say these states are different ways the string can "vibrate". That is a nice analogy and all, and it sells books, but it's not what string theory actually describes.

Finding proper analogies for theories in physics is hard, as pointed out by xkcd. But a better analogy is, perhaps, the energy states of an atom. As you might know, an electron in a hydrogen atom can be in the ground state (i.e. the lowest-energy state), and if you give it some energy it can be "excited" to a higher-energy state. The states of a string are somewhat like this. A string can be in its ground state and it may be excited to a higher-energy state. The set of all possible states is the so-called string spectrum.

Sometimes the spectrum is described as "an infinite tower of states", even in technical literature. Perhaps a more accurate description will be "an infinitely long and infinitely branching tree of states". But this is as far as I can go without writing any equations.

Wait a minute, you say; the Standard Model of particle physics only has 17 elementary particles, but string theory has infinity! Seems like we're missing "a few". Well, turns out that these "extra" particles are "conveniently" hidden at very high energies which we cannot access using existing particle accelerators or any other experiment in the foreseeable future. So, there you go.

Summary

Let's sum up here:

Strings in string theory are not "made of" real stuff, they are what (hypothetically!) makes up real stuff.
Strings are 1-dimensional fundamental entities, a direct generalization of 0-dimensional particles. In fact, there's no reason to stop at 1, and string theory also describes branes of 2 and more dimensions.
Strings trace out a 2-dimensional worldsheet in spacetime, on which one may perform calculations.
Strings are quantum objects and can be excited to any of an infinite number of excited states, corresponding to different types of particles.
Bonus question: Are strings "real"?

Here's a bonus question (and answer) for those who survived this far: Are strings "real"? By that I mean, in a universe that is described by string theory (which may or may not be similar to our own universe), are strings "real" in any sense of the word?

This is very similar to the question of whether the fields described by quantum field theory (QFT for short) are "real". For the uninitiated: QFT postulates quantum fields that exist in all of spacetime. Excited states of these fields are particles. Moreover, each field corresponds to a particular type of elementary particle.

So for example, all photons in the universe are excited states of a single field called the photon (or electromagnetic) field, all electrons are excited states of the electron field, and so on. I talk a bit about this in my answer to What is the relationship between a particle and a field? and also in my answer to What is the Higgs Mechanism?.

QFT is a mathematical model that describes our universe (and does so very well). String theory is also a mathematical model, meant to extend QFT. So asking whether fields exist or not, within the QFT framework, is the same as asking whether strings exist or not within the string theory framework. For the answer I refer you to my answer to How do scientists prove fields exist?.

ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ QUORA 21/6/2017