Quantum Field Theory

Elementary particles are not individual objects, but excitations of underlying fields that pervade all of space and time

Required:

• The Standard Model

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Quantum field theory (QFT) is the foundation of particle physics. It suggests that at the quantum scale, subatomic particles aren’t small physical objects, but excitations within quantum fields.

Fields

First, to describe a field, think of the mathematical grid that exists when someone makes a video game. The objects can only exist by specifying their location relative to the underlying grid. While you can’t see the grid in a video game, it is essential to the location of objects.

Quantum fields are a bit like this grid in a video game.

They exists everywhere and at all times. The grid scale is based on the theoretical smallest divisible length in our universe. At distances smaller than this length things seem to teleport, like they are snapping to a grid.

The idea of a mathematical grid that is omnipresent is known at a Cartesian Grid, thought of by Rene Descartes. It was originally used to express geometric shapes algebraically.

Excitations

Each particle in The Standard Model has it’s own corresponding quantum field. All of these different fields coexist simultaneously at every point in space, even in vacuums.

Imagine each line in these fields are like a guitar string, and can be plucked. When the field vibrates at a specific coordinate, we treat it as a corresponding particle.

For example, an electron is an excitation in the electron field, while a photon is an excitation in the electromagnetic field.

In our standard model, we would treat these field excitations as the particles we all know and love.

This behaivor to seemingly be a wave and a particle at the same time is called the x Wave-particle duality. However, in reality there are no particles, there are only fields and Quanta.

Quantization of fields

To describe the behavior of particles, fields in QFT are quantized.

Quantization is the process of turning what would be continuous, wave-like fluctuations into discrete energy levels. Basically, it’s adding ticks to the grid.

Quantization is used commonly in computing. It is the difference between ‘analog’ and ‘digital’ signals. When your music is digitally recorded, the sound waves are quantized into digital bits. A camera quantizes light waves into distinct pixels.

Quanta are the smallest divisible excitation of the field.

When enough energy is added to a field in a particular way, it creates a local, particle-like excitation. This excitation is what we call a Quantum (The singular form of Quanta).

• A photon is a quantum of the electromagnetic field.
• An electron is a quantum of the electron field.
• A gluon is a quantum of the gluon field, and so on.

Field Energy → is quantized into → Quanta → which behave like → Particles

Particles are not tiny objects floating in space but are actually localized excitations or “ripples” in their corresponding fields. They only behave as particles when they are quantized.

Fluctuations

Quanta occur because the quantum fields inherently contain energy. This is referred to as Zero-Point Energy. The x Heisenberg Uncertainty Principle dictates that it’s impossible for both the position and momentum of a system to be precisely zero.

This indicates that even in a complete vacuum, there will still be Quantum Fluctuations within the fields. This seemingly random energy is known as Quantum Uncertainty.

Virtual Particle Pairs

Most often, these fluctuations manifest as virtual particle-antiparticle pairs that briefly come into existence and annihilate each other almost immediately.

These fluctuations are happening everywhere all the time.

Particle Creation

Also called vacuum excitation, this is when a quantum fluctuation creates a real, observable particle instead of a virtual pair that immediately annihilates itself. This process must adhere to energy conservation, so the energy of the particle must come from somewhere, or be taken from the underlying field itself.

The fact that particles can spontaneously materialize even from a vacuum leads to some interesting thought experiments, such as the Boltzmann Brain.

Hawking Radiation

Quantum fluctuations, while being the smallest occurrence in our universe, have the power to take on the most massive objects - black holes - through a process known as Hawking Radiation.

Interactions

Quantum fields have creation and annihilation operators that allow for the discrete creation or destruction of quanta.

During an interaction, one field can “emit” a quantum, and another field “absorbs” it.

For example: When two electrons repel each other, one electron emits a virtual photon, which is then absorbed by the other electron. This exchange imparts a repulsive force due to the electromagnetic interaction.

This process doesn’t involve particles directly “touching” each other. Instead, they interact by exchanging quanta, which temporarily exist and transmit forces without any continuous medium. Remember, the “particles” exchanging quanta, are also just quanta themselves on their respective field.

These quanta exchanges are the basis of Gauge Bosons in The Standard Model.

Superposition

Energy Field values can exist in a mixture of different energy states.

The superposition state is represented by a wave function that includes all possible quantized energy levels. Because of quantum uncertainty, The actual energy state exists in a probability space instead of a concrete value.

When observed, the wave function collapses to a quantized value with a measurable energy value.

Superposition is the basis of the x Quantum Soup, where we explore the implications of the unobserved universe being a possibility space instead existing in a measurable state.

Implications

The fact that fields quantize into discrete, particle like excitations - instead of remaining continuous at infinitely smaller scales, indicates that there is a minimum discrete “bit” of the universe. The implications are almost.. digital.

If you try to dividing your computer screen in half over and over, you would eventually reach a point where you only have a row of pixels and can no longer divide in half again. Same with the data on your hard drive. You would eventually get to a binary bit, where no further downsizing can occur.

Our universe has a similar endpoint built in, called Planck Length. The bit size of the universe. There is another strange limit built into the universe, with all sorts of side effects, called Causality.