String Theory Explained: A Brief Overview Everyone Can Understand

String Theory is one of the revolutionary and most controversial concepts in physics that aims to unify all of the particles and fundamental forces of nature into one single theory.
Jaime Trosper

Over the centuries, we have viewed the universe through many different lenses, our models and theories have shifted and given way to new, revolutionary ideas. Not all of them wind up being correct (or even in the realm of possibility), but no one should ever be able to argue that physics is boring, Perhaps one of the singularly most interesting, not to mention complex, concepts to come out of theoretical physics is string theory. 

To understand string theory, there are several things we must explore first, beginning with quantum physics. In traditional physics, we have so-called point particles and extended particles. The Standard Model of Particle Physics, which is the definitive starting point to all things subatomic, tells us that every particle known to exist is an extended particle except for three: quarks, bosons, and leptons. One exception is the electron.

Extended particles don't have a well-defined surface, instead, they are more like the atmosphere of the Earth, which is the thickest near the surface of the Earth and it gets thinner with altitude. Extended particles have a size, but the boundary or exactly where an extended particle ends is fuzzy. 

Fermi Lab ponders, "Point particles are much more bizarre and are sometimes said to have zero size. This statement has raised more than one eyebrow. How can something have no size at all? And if it has mass, does the zero size mean it has infinite density?" The answer to that is no, for the record, but that's just one of the many mysteries surrounding point particles; They do, however, sometimes exist in quantum states that give them mass and charge.

It wasn't until we started slamming particles together at extremely high speeds that we began finding and classifying all of these different types of particles - the Higgs Boson should come to mind. We found that these elementary particles can be broken down into their further constituent parts, like quarks. Some, like baryons, exhibited characteristics of mass and spin (a baryon is a member of the quark and fermion family, which means it participates in one of the four forces: the strong interaction - something scientists were struggling to understand at the time).

However, the finding that really kick-started research into string theory was the discovery of a strange particle called the hadron.

Per the Cern Courier, "In the mid-1960s we theorists were stuck in trying to understand the strong interaction. We had an example of a relativistic quantum theory that worked: QED, the theory of interacting electrons and photons, but it looked hopeless to copy that framework for the strong interactions. One reason was the strength of the strong coupling compared to the electromagnetic one. But even more disturbing was that there were so many (and ever-growing in numbers) different species of hadrons that we felt at a loss with field theory – how could we cope with so many different states in a QED-like framework? We now know how to do it and the solution is called quantum chromodynamics (QCD)."

QCD, which was first developed in the '70s, is what pushed the concept of the strong force to emerge. It and quantum electrodynamics are closely linked. Both are considered to be examples of a special class of quantum field theories known as gauge theories - whereby particles theoretically interact as a result of the exchange of gauge bosons: "the photon for the electromagnetic force, W and Z bosons for the weak force, and gluons for the strong force." All, in turn, help comprise the all-important Standard Model of particle physics. Bringing us to...

The first version of string theory starts to come together:

String theory as a whole has many objectives: perhaps most importantly, it hopes to produce a "Theory of Everything," which includes figuring out how gravity works on a microscale. We've made some progress in that department, but here's a look at how it really got its start and how everything came together:

Gabriele Veneziano is the person who developed much of the framework for what would become string theory. He wrote an extremely important paper in 1968 that sent shockwaves through the theoretical physics community, It was called "Construction of a crossing-symmetric, Regge behaved amplitude for linearly-rising trajectories.

He worked for over a year, looking to develop some kind of theory to explain how the strong nuclear force (believed to bind protons and neutrons together, along with the constituent quarks and gluons inside protons and neutrons) interacted with hadrons. His work was largely mathematical in nature, but his calculations were enough to energize the community to better understand the implications of his original paper. 

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A few years later, three theoretical physicists - Yoichiro Nambu of the University of Chicago, Holger Nielsen of the Niels Bohr Institute, and Leonard Susskind, of Stanford University - made a huge discovery. Veneziano's mathematical proofs and general work trying to marry the strong force with the other forces could work if point particles were changed to string-like objects, which could contract, stretch and even vibrate. 

String theory replaces all matter and force particles with vibrating strings that twist and turn in complicated ways and which look like particles from our perspective. For example, a string can fold and vibrate in such as way as to gain the properties of a photon, while another string folded and vibrating a different way has the properties of a quark, etc.

The problem with this theory was that it would require 26 different dimensions and it requires a particle to exist with no mass that travels faster than the speed of light - called a tachyon (which remains a theoretical particle to this day) to make his work consistent with relativity and quantum theory. 

The three scientists mentioned above were among the first to suggest that changing particles to small loops would solve some of the problems with Veneziano's model. So what are these small strings made of, you may ask? Well, the answer is nothing really - the strings themselves make up everything.

One lingering problem was that the original version of string theory lacked an explanation for fermions, which have half-integer spin. That is until Pierre Raymond entered the picture and helped bring forth string theory 2.0.

Raymond reformulated string theory to include particle spin, allowing bosons, fermions and other particles with integral spins to join the club. Additionally, two other physicists, John Schwarz and Andre Neveu - from Princeton University - changed the game further by creating a version of string theory that didn't need to be consistent with quantum theory or special relativity. It also removed the need for the tachyon and 26 dimensions from the picture, dwindling the number of needed dimensions down to 10. This became known as the superstring theory. 

A look at superstring theory:

Superstring theory (or sometimes called supersymmetric string theory) adds a few extra parts to the original theory, like doubling the number of particles in the standard model and replacing a few other parts. For instance, it says that all known particles can basically be divided into two types: fermions and bosons. The catch is, these two particles are very dependent on each other - there must be a boson for every fermion and a fermion for every boson. To add to it, every known and still-unknown-to-us particle must have its own "superpartner."

Symmetry magazine notes, "In the early 1980s, theorists realized that the Standard Model itself could be made supersymmetric and that this extension would resolve some vexing problems with the theory. For example, the small mass of the Higgs boson is notoriously difficult to explain—its calculation requires subtracting two very large numbers that just happen to be slightly different from each other."

Elodie Resseguie, a postdoc at the US Department of Energy’s Lawrence Berkeley National Laboratory adds, "But if you add supersymmetry, this takes care of all these calculations such that you can get a light Higgs mass without needing to have such luck."

The biggest implication is that you can replace zero-dimensional elementary objects with 1-dimensional elementary constituents, or strings. The universe from the vantage point of superstring theory basically tells us that everything is fundamentally composed of these tiny strings. We perceive these strings to be particles based on how they vibrate when they are looped together, sorta like playing different notes on a violin or guitar.

It's important to note here that not all of the strings are looped together. Some of them are open (with two ends), while two other strings become twisted together, forming closed strings. A bit of tension must exist to help give rise to different modes of vibration, thus we can interpret these vibrations as elementary particles. 

String Theory Explained: A Brief Overview Everyone Can Understand
Open string vs closed string (Source: Xoneca/Wikimedia Commons)

Remember how I said that the mathematics for string theory originally only work with 26 dimensions of spacetime, but that was inevitably dropped to just 10 with superstring theory? That still sounds bonkers to people who appear to live in a reality with 3 spatial dimensions and one temporal dimension, but hopefully, we can make those extra details easy to understand.

History of extra dimensions and an understanding;

Two of the first people to suggest there may be extra dimensions - the originators of what would become known as the Kaluza-Klein theory - also happen to have helped lay the groundwork for string theory itself when they began working to unify electromagnetism with gravitation. For their work, they suggested that there exists not four, but five dimensions of space, However one of them is drastically different from the others, In fact, it might be curled in on itself through a process called compactification. It further implies that this compacted dimension only has gravity, and no electromagnetism, 

David Berman, a Reader in Theoretical Physics at Queen Mary, University of London, puts it into perspective: "We are used to living in four dimensions. If you are arranging a meeting then you need to give one more piece of information: the time of the meeting, say 3 pm. With four coordinates you can describe any event. We don't tend to clump time with the spatial dimensions but if you think about it, any event really happens in a spacetime with four dimensions. You can measure differences in time just like you can measure differences in space – we measure differences in space with a ruler and we measure differences in time with a clock. So anything you can think of in terms of space you can think of in terms of time."

"We can learn a lesson from this: our human perception of dimensions is limited. We only perceive three dimensions. We can understand that time is an extra dimension, an extra location for any event, but we don't see time in the same way. We experience it very differently from spatial dimensions as human beings. This hints that human perceptions of things may not be the end of the story in terms of what's possible."

"Mathematically the number of dimensions is just the number of coordinates you need to specify a point. We're familiar with specifying points in four-dimensional spacetime, but can you imagine a space where you need five bits of information? Or six? Or seven…? Mathematicians regularly work in higher dimensional spaces, but they are not the only ones. For example if you're a sound mixer making music you might be working with 12, 24, or even 128 tracks. At each moment in the music each of the, say, 24 tracks has a specific volume, defining a point in a 24-dimensional space of sound. The number of dimensions is just the number of bits of information you need to specify a point."

Confused? Yeah. Kaluza and Klein's research didn't immediately become the subject of speculation - its explanation for quantum gravity was weak. Moreover, as quantum physics further developed, it didn't account for the strong and weak nuclear interactions. However, new life was breathed into it when the Yang-Mills theory was developed in the 1970s. This was an attempt to unify all the fundamental forces except gravitation - ultimately unifying the weak nuclear interactions with electromagnetism. It can be thought of as the most symmetric field theory that does not involve gravity.

Other theories then started taking shape... Like,

String theory on steroids: Superstring theory

Superstring Theory, or supersymmetric string theory, is what you get when string theory and the concept of supersymmetry combine. If you're not familiar with supersymmetry, gather round..

In the standard model of particle physics, there are essentially two groups of fundamental particles: We call them bosons and fermions. The former mediate the fundamental forces as integer spin particles. while the latter have half-integer spin and comprise matter. 

Most theoretical physicists believed the bosons and fermions to be connected in some way, but the math suggested otherwise. This is why the idea of supersymmetry was born.

As a primer, check out the video below, where an expert from Fermilab helps explain how the concept of supersymmetry works in the most simplistic way possible:

According to Cern, "Particles like those in the Standard Model are classified as fermions or bosons based on a property known as spin. Fermions all have half of a unit of spin, while the bosons have 0, 1 or 2 units of spin. Supersymmetry predicts that each of the particles in the Standard Model has a partner with a spin that differs by half of a unit. So bosons are accompanied by fermions and vice versa. Linked to their differences in spin are differences in their collective properties. Fermions are very standoffish; every one must be in a different state. On the other hand, bosons are very clannish; they prefer to be in the same state. Fermions and bosons seem as different as could be, yet supersymmetry brings the two types together."

It does this with a new particle, the Higgs boson. While the Standard Model seems to predict that all particles should be massless, this is at odds with experimental observations. The Higgs boson provides this mass. At the same time, "the extra particles predicted by supersymmetry would cancel out the contributions to the Higgs mass from their Standard-Model partners ...The new particles would interact through the same forces as Standard-Model particles, but they would have different masses. If supersymmetric particles were included in the Standard Model, the interactions of its three forces – electromagnetism and the strong and weak nuclear forces – could have the exact same strength at very high energies, as in the early universe."

The new theory also predicted most of the known particles and a new spin-2 particle, the ‘graviton’, which is a candidate for gravitational force-carrier.

Over time, physicists came up with five different versions of Superstring Theory, namely Type I, Type IIA, Type IIB, Heterotic, and Heterotic with E(8) x E(8) gauge symmetry.

The first superstring revolution attracted a lot of attention. In 1995, Edward Witten, a theorist at the Institute for Advanced Study in Princeton, New Jersey, argued that the five string theories actually each represented an application of a more fundamental, 11-dimensional theory. This unified approach is popularly called ‘M-theory’.

Extra-dimensions of string theory

We left our discussion on extra-dimensions incomplete while talking about Superstring Theory. Let’s continue.

String Theory supports 10 dimensions, 3 of which extend indefinitely and are observable to us. So, where are the other 6 spatial dimensions?

They are right here but curled upon themselves, i.e. they are compactified.

The extra-dimensions are inherent in the mathematical notion of ‘manifold’. Take, for example, a relatively large sphere, and place an ant over it.

The surface of the sphere will look flat to the ant. So, we have a ‘local’ shape (flat surface) and a ‘global’ shape (the sphere) here. The sphere, in this case, is an example of a 2-dimensional manifold.

It is the same with our world.

We live in a 3-dimensional manifold. Even if we do not consider the postulates of String Theory, general relativity suggests a fourth dimension, gravity, and the universal phenomenon is described with the help of curvature of this additional dimension.

Thus, we can easily conclude that a manifold may have curvature and other non-trivial properties.

String Theory Explained: A Brief Overview Everyone Can Understand
Source: Andrew J. Hanson/Wikimedia Commons

A Calabi-Yau manifold is a class of 6-dimensional manifold and is a subject of study in String Theory. They wonderfully predict several realistic theories in 4-dimensional spacetime.

We have drawn heavily from the earlier discussed Kaluza-Klein idea of compactification. The extra dimensions are just compact manifold which is too small to be detected by us.

Furthermore, M-theory extends on string theory’s 10 dimensions and works with a total of 11 dimensions.

In Closing: Is string theory really a "theory of everything?"

The Standard Model of Particle Physics, while a very important part of understanding how the universe works on a microscale, still isn't completely without flaws. Yet, it's definitely our greatest tool when it comes to putting together a decisive model of string theory. 

Most importantly, we have quantum mechanics, general relativity, quantum field theory and many more models to gain insight on the same subject that is the Universe.

Can’t they all be connected in some way? Shouldn’t quantum mechanics and gravitation come under a common framework? Yes, they should.

The Theory of Everything is our attempt to unify different theoretical models to probe Nature. String Theory came out as the strongest candidate for such a unified approach.

It has unexpectedly predicted the quantization of gravity with gravitons. So, why isn’t it the ultimate discovery?

String Theory has been somewhat successful in explaining many complex phenomena, most importantly black holes. Black holes are very small objects with very large mass and it requires general relativity as well as quantum states to study them.

String Theory has also offered new insights into quark-gluon plasma and a relationship between quantum field theory and string theory has been established, called AdS/CFT correspondence.

String Theory has produced numerous results, some of which may seem absurd or incomprehensible. For example, it has been used to predict the existence of 10500 universes or a massive multiverse.

However, String Theory has faced many setbacks. String Theory models rely on supersymmetry which, like the extra dimensions, has yet to be observed. The models are also criticized for their inability to adequately describe an expanding universe. 

But what startles the scientific community is the recurring comeback of this controversial theory. Perhaps largely to do with the usefulness of the mathematics involved, which has highlighted connections between different areas of math, inspiring many new ideas and approaches.

String Theory has been the object of interest in the media and popular science as much as in the scientific community for its counter-intuitive solutions. The biggest problem with String Theory, however, is that most of its predictions and notions can’t be tested with experiments, as they require very high energy, which is currently not possible with the tools we have.

But String Theory can also be thought of as a revolution in the world of physics, and it is likely to be a part of mainstream physics in one way or another. 

So, here is String Theory simplified.

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