Quantum Field Theory for Dummies
The easiest explanation of the most beautiful quantum theory of reality
“I had set out to disprove quantum field theory — and the opposite occurred! I was shocked.”
— David Gross, theoretical physicist and Nobel laureate
When we were in school, we were taught that every matter is made up of tiny little particles called atoms having a concentrated central mass called the nucleus. The nucleus contains positively charged protons and chargeless neutrons. There are electrons also that revolve around the nucleus. If you are a University student, this same thing is taught in a slightly different and a little more advanced way, that the protons and neutrons are not elementary particles as they are further made up of quarks. This means that the universe is made up of a combination of electrons and quarks. But is it completely true?
Let’s try and understand this. The universe isn’t just made by electrons and quarks because in this model we cannot know how different forces work and what these quarks, electrons, etc are made of. We often prefer to talk about string theory, quantum mechanics, and the topics such as multiverse because we have heard about these terms at some point somewhere and we find these topics very fascinating. But there is also one such theory about which most of us do not know, or at least don’t understand. This theory is quantum field theory.
In order to understand the universe, quantum field theory is one of the best theories because most of the predictions made by QFT have turned out to be true and it works best to describe most of the physical phenomena and the behavior of the universe to a great extent. Conventionally, QFT is often regarded as a complicated concept. In this article, I shall try to explain the basics of Quantum field theory in as simple and understandable a manner as possible.
Before we start to learn about QFT, let’s try and understand what the Standard Model of particle physics is. There was a time when scientists believed that atoms are the smallest particles of matter and that they cannot be further divided. Then we understood that atoms aren’t really the smallest particles and they are made of sub-atomic particles- protons, neutrons, and electrons. When quantum theory came into play in the mid-1930s and 40s, it predicted the existence of new particles, which we weren’t familiar with so far. In order to understand these newly predicted particles, we needed some new theories. When these new theories were formulated, they predicted the existence of some more elementary particles. Later when we smashed the already existing particles in the high-energy particle accelerators, we discovered new predicted particles. With the increasing discoveries of new and new elementary particles, we had to categorize them into different categories based on their properties like mass, spin, electric charge, etc. This gave birth to a model that could fit in all the fundamental particles divided according to their intrinsic properties. The model not only arranged these particles but also provided a way to explain the fundamental forces of nature with regard to their corresponding force carriers. This model is famously known as the Standard Model of Particle Physics.
Let’s understand what these particles are in this model and what their roles are in the universe. All the particles present in the universe are mainly divided into two categories: Bosons and Fermions. Fermions are responsible for constructing the matter, be it a table, a tree, a book, or an animal. Whereas Bosons are the force carriers. The Fermionic family is further divided into Quarks and Leptons. There is a total of six different types of quarks: Up, Down, Charm, Strange, Top, and Bottom. They form protons and neutrons inside the nucleus of an atom. Quarks aren’t stable particles hence they combine in a group to form Hadrons. Hadrons are further divided into Mesons and Baryons. Baryonic particles (protons and neutrons) are formed by the combination of three quarks. Protons are made of two Up and one Down Quark whereas neutrons are made of two down and one up quark. The remaining four types of quarks combine together to give us other new particles. Leptons, on the other hand, are those particles that aren’t formed by quarks, like muon, electrons, tau, neutrino, etc. These are stable particles and hence they don’t have to combine with one another to form other particles and they can exist independently.
Heisenberg’s uncertainty principle predicts the existence of those particles which exist without any cause, and their existence is probabilistic. Such particles are called virtual particles. Such virtual particles are experimentally found. Irrespective of how weird these particles are, they always tend to follow a certain specific pattern. These particles always come in pairs. Such pairs contain two types of particles out of which one is a regular matter particle and another is an anti-matter particle. Anti-matter particles are those particles that have the same mass as matter particles but are opposite in charge. When an electron is formed, an antimatter particle is also formed alongside which is called a positron, or a positive electron. When these matter-antimatter particles collide, they annihilate to produce pure energy. Like electrons, all the other leptons also have their antimatter pair. Bosons are of four types: Photons, W/Z bosons, gluons, and gravitons. Till the early 19th century scientists used to believe that electricity and magnetism are two different forces. Now we know that these two forces are just different forms of the same force called electromagnetic force. Electricity, visible light, and so on are the results of electromagnetic force. This force is carried by photons. We experience this type of force every single day in our lives one or the other forms. The weak nuclear force is the second weakest force of all which is responsible for beta decay. W/Z bosons are responsible for carrying this force. The strong nuclear force is the strongest force of all which is responsible for binding the nucleons (protons and neutrons) together in the nucleus of an atom. Gluons are the particles responsible for carrying strong nuclear force. The gravitational force is the weakest of all fundamental forces which are hypothetically carried by gravitons. Unfortunately, we haven’t discovered the existence of any such particles but their existence has been predicted by many prominent theories. So far we have learned about the matter particles and the force carries in the standard model. There is, however, one more type of particle in the list called the Higgs Boson, which is primarily responsible for providing mass to the other particle. I shall share the story about the Higgs Boson in some other issue.
The force carrier particles, Bosons, were predicted by Quantum field theory. As the name suggests, quantum field theory is the combination of quantum mechanics and field theory. Classical mechanics is more of a game of determinism, which means that with the past information we can tell a great deal about the future. Quantum mechanics, on the other hand, is all about probabilities. The act of measurement, in quantum mechanics, alters the reality of physical phenomena. The combination of all possible outcomes of a particle is known as a wave function which can be understood as the intrinsic properties of the quantum particle like position, momentum, speed, and so on. An ordinary individual observes the materialistic world but a scientist, particularly, a physicist observes a world with matter and fields. Empty space, in physics, is not necessarily empty. Let’s try and understand it with a simple example when you try to join the like poles of a magnet together, you experience a sort of repulsive force. The region between the magnets is seen as empty but we still experience some sort of force acting in there. The space that is seen as empty actually contains a magnetic field in it. Likewise, empty spaces in the universe aren’t really empty, they have fields in them. This is the basic idea of the field theory.
Now when you combine quantum mechanics and field theory, it gives rise to quantum field theory which states that everywhere in this universe and at every instant of time there is the existence of different types of fields that we cannot see like a magnetic field, electric field, gravitational field, etc. In fact, every elementary particle has its own field like the Higgs field, electron field, quark field, etc. Physicists represent these fields by numbers. We see one or more such numbers in every point of space. The fields are divided into multiple types depending upon how many numbers a field requires. For instance, the Higgs field is a scalar field because at every point of space it requires a single number to describe this field. Electric and magnetic fields are vector fields as they need both magnitude and direction for their complete description. According to Sir Isaac Newton, the gravitational field is a vector field whereas according to Einstein it is a tensor field. When these fields are provided with energy, they go to higher energy states forming sort of like rippled like in water. These ripples thus formed are called particles. For instance, when ripples are formed in the electron field then electrons are formed. Likewise, ripples in quark fields give us quarks. When these ripples become silent then the corresponding particles also disappear. At the point at which we give the energy in these fields, the particle is formed at that point and as that energy starts to spread across the field, we say that the particle is moving. For some fields, we need to provide a great amount of energy in order to produce the particles. Some fields require less energy to generate the particle. The primary factor that determines how much energy a field requires in order to produce a particle depends upon the mass of the corresponding particle associated with the field.
For example, Higgs bosons are a lot heavier than electrons. Hence, the Higgs field requires a huge amount of energy for generating these particles. We can do that only in particle accelerators like the Large Hadron Collider. So far we have understood the generation of different particles in terms of fields. Now let’s understand how the fundamental forces work according to the quantum field theory.
The fields exist at the same place in space and time due to which we often see the exchange of energy between and among various fields. That is how the forces work and due to this phenomenon sometimes one particle gets converted into another. This is one of the best theories to understand nature and reality at the quantum level so far. There are still many questions associated with Quantum field theory. It hasn’t been able to explain the existence of dark matter and dark energy. Many physicists believe that dark matter is also a result of energy in some fields which we do not understand yet.
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