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Updated April 28, 2023

Field concept in physics

Each wavelet represents the energy of the field of water molecules

Image: A physical field is created by an energy source that generates an influence on the surrounding space.
This source can be the air temperature for the temperature field, the wind speed for the wave field, a pressure gradient for the acoustic field, a charged particle for the electromagnetic field, a mass for the gravitational field, radioactivity for the ionizing radiation field, etc.
All of these energy sources can be represented by fields.

Approximate image of a field

The notion of field in physics is abstract and cannot be represented by an image. However, one can get a superficial idea of the concept of field.

A field is a delimited portion of space filled with measurable physical quantities which can vary over time.

For example :
• In a room, at every point in space and at every moment, it is possible to measure physical quantities that characterize the state of the room, such as temperature, pressure, density, etc. The room is therefore filled with a temperature field, a pressure field, a density field, etc.
These fields are called scalar because each point is represented by a real or complex number.

• At each location in the room and at each instant, there is also a movement of air molecules that can be measured by two values, a direction and a speed.
This velocity field is said to be vector because each place is represented by a quantity which has a direction and a magnitude. This quantity is a vector, graphically, an arrow. The length of the arrow represents the magnitude of the vector, in our case, the speed. The direction of the arrow represents the direction of the vector.

In classical physics, if one wishes to represent a field by an approximate image, the simplest thing is to imagine a liquid expanse, a lake for example.
At each place and at each moment, there is a movement of water molecules that can be measured by a vector value.
When the lake is in its state of equilibrium, that is to say in its state of lowest energy that can be called the fundamental state, nothing happens, it is flat calm. Each vector v = [x, y] has a zero component, i.e. v = [0, 0]. The velocity field of water molecules is still, empty, flat, and invisible in two-dimensional space.
If the wind picks up, energy will be brought to the lake, the water molecules will stir and discernible ripples will form.
Each water molecule speed will become measurable by a non-zero vector. Each vector will represent a source of energy that generates an influence on the surrounding space. While the field was empty, flat and invisible, it will manifest and appear in three dimensions. A physical field is then created. In other words, the physical field can be seen as a manifestation of the presence of an energy source. The field does not directly represent the source but allows us to describe, in our case, how the physical properties of the lake vary at each point in space.

In quantum physics, fields are more complicated to imagine.

For example :
• The electromagnetic field is created by moving electrical charges, such as electrons, which are a source of energy. In this case, the field itself represents the distribution of electric and magnetic fields in space. The electromagnetic field is a combination of electric and magnetic fields that propagates through space in the form of electromagnetic waves.

• The quantum field of electrons is spinorial, at each place and at each instant, one can measure the behavior of the spin of the electron by a spinorial wave function. It is a complex mathematical function that characterizes the quantum state of the electron as a function of its position, time and spin. Quantum motions of the electron, such as its spin, also create magnetic fields. Spin is an intrinsic property of particles that is related to their magnetic moment.

In conclusion, The quantum field of electrons, photons, protons, and all elementary particles, is an important theoretical concept for understanding the quantum properties of systems where all the fundamental fields of particles overlap.
When all of these fields are in their lowest energy, ground state, we are in the quantum vacuum, a calm sea filled with all energyless, undetectable particles. However, the quantum vacuum is not an "absolute nothingness", because it constantly fluctuates and gives rise to ephemeral pairs of particles called "virtual particle pairs". These pairs of virtual particles appear and disappear so quickly that their net effect on spacetime is negligible. These vacuum fluctuations can be interpreted as a quantum field that exists even in the absence of real particles. It will be enough to bring a source of energy to this quantum field so that a wavelet of the vacuum, a particle, arises.

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