concept

field

A physical quantity assigned to every point in spacetime, such as an electromagnetic or gravitational field.
21 related articles · 1 formulas

Description

A field in physics is a physical quantity that has a value at every point in space and time. The most familiar examples are the electromagnetic field, which describes the force on a charged particle at any location, and the gravitational field, which describes the pull on a mass. Fields are not just mathematical conveniences; they carry energy and momentum, can ripple as waves (like light), and in quantum physics, they are the fundamental entities from which particles emerge as excitations.

History

The field concept was developed in the 19th century by Michael Faraday and James Clerk Maxwell, who described electric and magnetic forces as mediated by fields rather than by action at a distance. It was later generalized by Albert Einstein's general relativity, where gravity is the curvature of spacetime itself, and by quantum field theory in the 20th century.

How it works

A field assigns a number, vector, or more complex object to each point in spacetime. For instance, the temperature in a room is a scalar field, while the wind velocity is a vector field. In modern physics, fields are dynamic: they can fluctuate, propagate disturbances, and interact with particles. In quantum field theory, each particle type corresponds to a field, and particles are quantized ripples in that field — for example, a photon is a ripple in the electromagnetic field.

In practice

Fields are used in virtually all of physics and engineering, from calculating the trajectory of a satellite in Earth's gravitational field to designing antennas that emit and receive electromagnetic fields for communication.

Fun fact

The vacuum is not empty: in quantum field theory, it is a seething sea of temporary particle-antiparticle pairs popping in and out of existence, a phenomenon called vacuum fluctuations.

Concept graph →

Formulas

$$\Psi = \int \mathcal{D}\phi\, e^{iS[\phi]/\hbar}$$
Quantum amplitude is sum over histories with phase from action.
What is in the formula
Ψvariablequantum amplitude (transition amplitude or wavefunction) — probability amplitude varies
φvariablefield configuration (path variable) — field varies
S[φ]variableaction functional of the field configuration — action joule second
ℏconstantSets the scale of quantum fluctuations — reduced planck constant = 1.054571817e-34 joule second
∫ 𝒟φoperatorsums over all possible histories of the field — functional integral

Related articles · 21

Quantum Physics2026-08-041 minarXiv:2608.03549express
Gravity Muffles Light's Voice
Light escaping a massive body loses steam. Its frequency dips slightly, and its color shifts toward red. Physicists call this gravitational redshift. In classical theory, it's all clear, but the moment you bring quanta into the picture, trouble starts. Previously, this shift was modeled as a kind of mode mixer — a device that entangles different states of light.
Cosmology2026-07-282 minarXiv:2607.25317express
Current-Carrying Cosmic Strings and Their Gravitational Imprint
Right after the Big Bang, space cooled unevenly. In some places, folds could have formed — threads of energy as thin as a hair but incredibly dense. Physicists call them cosmic strings. They oscillate, collide, and emit gravitational waves — ripples in the fabric of space itself.
General Relativity2026-07-281 minarXiv:2607.26035express
The Universe as a Web of Quantum Connections
In the quiet of the quantum world, there is no emptiness. Particles are intertwined by invisible threads — entanglement. The authors of the work proposed that the very fabric of spacetime is woven from these threads. This is not just a metaphor: they built a mathematical framework where the distance between points is determined by how much shared information they hold.
HEP Phenomenology2026-07-271 minarXiv:2607.24930express
Gravitational Waves Turn into Light
A thrown stone sends ripples across water. A gravitational wave is the same kind of ripple, but in spacetime. It is produced, for example, by the merger of two black holes. In classical physics, this ripple is eternal: once created, it travels through the Universe without fading.
Strongly Correlated2026-07-262 minarXiv:2607.23547express
Quantum Magnet Reveals Hidden Symmetry
A pale green crystal was placed in a magnetic field and cooled below one kelvin — almost to absolute zero. Inside it hide chains of copper atoms that behave like tiny magnetic needles. Usually their orientation is chaotic, but the strong field and cold make the needles align in a unified impulse, like soldiers on a parade ground.
Quantum Physics2026-06-261 minarXiv:2606.28640express
Vortices in the Quantum World
A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.
HEP Theory2026-06-191 minarXiv:2606.21522express
Quantum Gravity Finds a Foothold in Symmetry
When a grain of sand falls on a table, its impact is predictable. But if you squeezed it down to the size of an atomic nucleus, the familiar laws of gravity would break down — the force of gravity would grow without bound.
General Relativity2026-05-312 minarXiv:2606.01052express
Gravitational Light Without Fire
Two massive spheres slowly drift apart in empty space. From the standpoint of ordinary mechanics, nothing special is happening. But Einstein's equations say otherwise: accelerating masses stir spacetime itself, and from them spread gravitational waves — ripples that stretch and squeeze everything in their path.
Cosmology2026-05-211 minarXiv:2605.22944express
Strings of the Cosmos: How to Catch the Universe's Tremors
A fundamental string plucked at the moment of the Big Bang doesn't just hum a single note — waves run along it, and occasionally tiny loops peel off. These loops, like tuning forks, begin to ring at their own frequency, producing a very high-pitched sound.
General Relativity2026-05-111 minarXiv:2605.10749express
How a fast particle wakes up the gravity of a massive body
A stone falls into a pond — ripples spread across the water. If the stone doesn't fall but whizzes over the surface at tremendous speed, a straight wave runs along the water. When it hits a floating log, ripples spread out from the point of impact. That's roughly how gravity works in the new study.
General Relativity2026-05-091 minarXiv:2605.08597express
The Formula Governing the Magnetic Fields of Stars
A magnetic field in plasma resembles a stretched soap film: pressure from inside pushes it out, while surface tension pulls it in, giving it shape. Here too, magnetic pressure and tension forces balance each other.
General Relativity2026-05-031 minarXiv:2605.01951express
Why a Charge Doesn't Glow in Gravity
A stone falls into a pond — near the shore, the ripples are barely visible, while the water churns at the point of impact. The electric field around a charge behaves similarly: close in, it's sharp and tangled, but at a distance it stretches into a smooth wave that carries energy away. Physicists call this distant region the radiation zone.
Quantum Physics2026-05-032 minarXiv:2605.05239express
Gravity Finds Its Way to the Quantum
A stone falls to the ground along the most economical route — the one that expends the least time and energy. This principle of least action governs all of classical physics. But in the microworld, everything jitters: fields fluctuate, and you can't say precisely where anything is.
Classical Physics2026-03-131 minarXiv:2603.13448express
The Invisible Ocean That Holds the Atom
According to ordinary mechanics, an electron in an atom should spiral into the nucleus and crash into it, like a surfer losing speed and falling off the board. But atoms live for billions of years. Because space isn’t empty. Even in absolute vacuum, an invisible electromagnetic sea ripples — the zero-point field. Its waves continuously nudge the electron.
Quantum Physics2026-02-261 minarXiv:2602.22715express
Can Gravity Repel? Quantum Superposition and Negative Weak Values
The familiar picture: gravity always attracts. But if a mass is in quantum superposition (that is, in two places at once, like an object in a double-exposure photograph) everything flips. Quantum theory allows a particle to be both here and there in a literal sense: its position is described by a wave function smeared across space.
Quantum Physics2026-02-121 minarXiv:2602.12266express
Gravity Can Push Away — A Quantum Experiment
Gravity always pulls — an apple falls down, planets orbit in circles. But by placing a source of gravity in two places at once, you can get the opposite. Physicists have proposed an experiment: a massive body is put into a quantum state, smeared across space like a cloud. Then a tiny particle is shot into that cloud.
Classical Physics2026-01-231 minarXiv:2601.17098express
How Waves Tell Us About the World
A stone drops into a pond — ripples spread across the water. Do short waves outrun long ones? No, in deep water it's the opposite: long waves overtake short ones. In metal, sound of one pitch travels at one speed, another pitch at another.
Quantum Physics2025-10-221 minarXiv:2510.19969express
Only Quantum Gravity Can Entangle Masses
Two massive spheres in the cosmic void. Push one, and the second will feel the push only after a moment: gravitational influence travels, like an echo of a shout in the mountains, with inevitable delay. This is how curved space transmits signals locally, step by step — predicted by Einstein long ago.
The Vacuum as Conductor: How Quantum Emptiness Rewrites the Properties of Matter
The hall is silent, but the conductor has already raised the baton. The orchestra is quiet, yet the score is changing. So it is in an optical resonator: there is no light, but the quantum vacuum—that emptiness filled with short-lived field fluctuations—is already conducting the…
Five Questions Physics Asks Philosophy
At night, an astronomer points a telescope at the edge of the visible universe and sees not stars but ripples — the imprint of the first moments. He knows these ripples should obey statistics, like the heights of people in a crowd. But he has only one crowd, and nothing to compare it with. This is cosmic variance.